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Journal articles on the topic 'Representation of algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Rouquier, Raphaël. "Quiver Hecke Algebras and 2-Lie Algebras." Algebra Colloquium 19, no. 02 (May 3, 2012): 359–410. http://dx.doi.org/10.1142/s1005386712000247.

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We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.

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2

Behn, Antonio, Alicia Labra, and Cristián Reyes. "Irreducible Representations of Power-associative Train Algebras." Algebra Colloquium 22, spec01 (November 6, 2015): 903–8. http://dx.doi.org/10.1142/s1005386715000759.

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Train algebras were introduced by Etherington in 1939 as an algebraic framework for treating genetic problems. The aim of this paper is to study the representations and irreducible representations of power-associative train algebras of rank 4. There are three families of such algebras and for two of them we prove that every irreducible representation has dimension one over the ground field. For the third family we give an example of an irreducible representation of dimension three.

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3

Goodwin, Simon M., Gerhard Röhrle, and Glenn Ubly. "On 1-dimensional representations of finite W-algebras associated to simple Lie algebras of exceptional type." LMS Journal of Computation and Mathematics 13 (September 2, 2010): 357–69. http://dx.doi.org/10.1112/s1461157009000205.

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AbstractWe consider the finiteW-algebraU(𝔤,e) associated to a nilpotent elemente∈𝔤 in a simple complex Lie algebra 𝔤 of exceptional type. Using presentations obtained through an algorithm based on the PBW-theorem forU(𝔤,e), we verify a conjecture of Premet, thatU(𝔤,e) always has a 1-dimensional representation when 𝔤 is of typeG2,F4,E6orE7. Thanks to a theorem of Premet, this allows one to deduce the existence of minimal dimension representations of reduced enveloping algebras of modular Lie algebras of the above types. In addition, a theorem of Losev allows us to deduce that there exists a completely prime primitive ideal inU(𝔤) whose associated variety is the coadjoint orbit corresponding to e.

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4

Benjumea, J. C., J. Núnez, and A. F. Tenorio. "Minimal linear representations of the low-dimensional nilpotent Lie algebras." MATHEMATICA SCANDINAVICA 102, no. 1 (March 1, 2008): 17. http://dx.doi.org/10.7146/math.scand.a-15048.

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The main goal of this paper is to compute a minimal matrix representation for each non-isomorphic nilpotent Lie algebra of dimension less than $6$. Indeed, for each of these algebras, we search the natural number $n\in\mathsf{N}\setminus\{1\}$ such that the linear algebra $\mathfrak{g}_n$, formed by all the $n \times n$ complex strictly upper-triangular matrices, contains a representation of this algebra. Besides, we show an algorithmic procedure which computes such a minimal representation by using the Lie algebras $\mathfrak{g}_n$. In this way, a classification of such algebras according to the dimension of their minimal matrix representations is obtained. In this way, we improve some results by Burde related to the value of the minimal dimension of the matrix representations for nilpotent Lie algebras.

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5

Zhou, Jian. "Representation Rings of Classical Groups and Hopf Algebras." International Journal of Mathematics 14, no. 05 (July 2003): 461–77. http://dx.doi.org/10.1142/s0129167x03001922.

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We prove a double coset formula for induced representations of compact Lie groups. We apply it to the representation rings of unitary and symplectic groups to obtain Hopf algebras. We also construct a Heisenberg algebra representation based on the restiction and induction of representations of unitary groups.

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6

Dräxler, Peter. "Normal Forms for Representations of Representation-finite Algebras." Journal of Symbolic Computation 32, no. 5 (November 2001): 491–97. http://dx.doi.org/10.1006/jsco.2000.0480.

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7

Gonçalves, Daniel, Hui Li, and Danilo Royer. "Branching systems and general Cuntz–Krieger uniqueness theorem for ultragraph C*-algebras." International Journal of Mathematics 27, no. 10 (September 2016): 1650083. http://dx.doi.org/10.1142/s0129167x1650083x.

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We give a notion of branching systems on ultragraphs. From this, we build concrete representations of ultragraph [Formula: see text]-algebras on the bounded linear operators of Hilbert spaces. To each branching system of an ultragraph, we describe the associated Perron–Frobenius operator in terms of the induced representation. We show that every permutative representation of an ultragraph [Formula: see text]-algebra is unitary equivalent to a representation arising from a branching system. We give a sufficient condition on ultragraphs such that a large class of representations of the [Formula: see text]-algebras of these ultragraphs is permutative. To give a sufficient condition on branching systems, so that their induced representations are faithful, we generalize Szymański’s version of the Cuntz–Krieger uniqueness theorem to ultragraph [Formula: see text]-algebras.

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8

Dräxler, Peter. "Representation-Directed Diamonds." LMS Journal of Computation and Mathematics 4 (2001): 14–21. http://dx.doi.org/10.1112/s1461157000000784.

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AbstractA module over a finite-dimensional algebra is called a ‘diamond’ if it has a simple top and a simple socle. Using covering theory, the classification of all diamonds for algebras of finite representation type over algebraically closed fields can be reduced to representation-directed algebras. The author proves a criterion referring to the positive roots of the corresponding Tits quadratic form, which makes it easy to check whether a representation-directed algebra has a faithful diamond. Using an implementation of this criterion in the CREP program system on representation theory, he is able to classify all exceptional representation-directed algebras having a faithful diamond. He obtains a list of 157 algebras up to isomorphism and duality. The 52 maximal members of this list are presented at the end of this paper.

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9

Gifford, James A. "Operator algebras with a reduction property." Journal of the Australian Mathematical Society 80, no. 3 (June 2006): 297–315. http://dx.doi.org/10.1017/s1446788700014026.

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AbstractGiven a representation θ: A → B(H) of a Banach algebra A on a Hilbert space H, H is said to have the reduction property as an A—module if every closed invariant subspace of H is complemented by a closed invariant subspace; A has the total reduction property if for every representation θ: A → B(H), H has the reduction property.We show that a C*—algebra has the total reduction property if and only if all its representations are similar to *—representations. The question of whether all C*-algebras have this property is the famous ‘similarity problem’ of Kadison.We conjecture that non-self-adjoint operator algebras with the total reduction property are always isomorphic to C*-algebras, and prove this result for operator algebras consisting of compact operators.

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10

Massuyeau, Gwénaël, and Vladimir Turaev. "Brackets in representation algebras of Hopf algebras." Journal of Noncommutative Geometry 12, no. 2 (July 2, 2018): 577–636. http://dx.doi.org/10.4171/jncg/286.

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11

BIRMAJER, DANIEL. "CONSTRUCTING FULL BLOCK TRIANGULAR REPRESENTATIONS OF ALGEBRAS." Journal of Algebra and Its Applications 06, no. 02 (April 2007): 259–65. http://dx.doi.org/10.1142/s021949880700217x.

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Every finite dimensional representation of an algebra is equivalent to a finite direct sum of indecomposable representations. Hence, the classification of indecomposable representations of algebras is a relevant (and usually complicated) task. In this note we study the existence of full block triangular representations, an interesting example of indecomposable representations, from a computational perspective. We describe an algorithm for determining whether or not an associative finitely presented k-algebra R has a full block triangular representation over [Formula: see text].

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12

Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.

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13

DAVIDSON, KENNETH R., and ELIAS KATSOULIS. "NEST REPRESENTATIONS OF DIRECTED GRAPH ALGEBRAS." Proceedings of the London Mathematical Society 92, no. 3 (April 18, 2006): 762–90. http://dx.doi.org/10.1017/s0024611505015662.

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This paper is a comprehensive study of the nest representations for the free semigroupoid algebra ${\mathfrak{L}}_G$ of a countable directed graph $G$ as well as its norm-closed counterpart, the tensor algebra ${\mathcal{T}}^{+}(G)$.We prove that the finite-dimensional nest representations separate the points in ${\mathfrak{L}}_G$, and a fortiori, in ${\mathcal{T}}^{+}(G)$. The irreducible finite-dimensional representations separate the points in ${\mathfrak{L}}_G$ if and only if $G$ is transitive in components (which is equivalent to being semisimple). Also the upper triangular nest representations separate points if and only if for every vertex $x \in {\mathcal{T}}(G)$ supporting a cycle, $x$ also supports at least one loop edge.We also study faithful nest representations. We prove that ${\mathfrak{L}}_G$ (or ${\mathcal{T}}^{+}(G)$) admits a faithful irreducible representation if and only if $G$ is strongly transitive as a directed graph. More generally, we obtain a condition on $G$ which is equivalent to the existence of a faithful nest representation. We also give a condition that determines the existence of a faithful nest representation for a maximal type ${\mathbb{N}}$ nest.

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14

Herschend, Martin, Osamu Iyama, and Steffen Oppermann. "n -representation infinite algebras." Advances in Mathematics 252 (February 2014): 292–342. http://dx.doi.org/10.1016/j.aim.2013.09.023.

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15

CEBALLOS, MANUEL, JUAN NÚÑEZ, and ÁNGEL F. TENORIO. "REPRESENTING FILIFORM LIE ALGEBRAS MINIMALLY AND FAITHFULLY BY STRICTLY UPPER-TRIANGULAR MATRICES." Journal of Algebra and Its Applications 12, no. 04 (March 10, 2013): 1250196. http://dx.doi.org/10.1142/s0219498812501964.

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In this paper, we compute minimal faithful representations of filiform Lie algebras by means of strictly upper-triangular matrices. To obtain such representations, we use nilpotent Lie algebras [Formula: see text]n, of n × n strictly upper-triangular matrices, because any given (filiform) nilpotent Lie algebra [Formula: see text] admits a Lie-algebra isomorphism with a subalgebra of [Formula: see text]n for some n ∈ ℕ\{1}. In this sense, we search for the lowest natural integer n such that the Lie algebra [Formula: see text]n contains the filiform Lie algebra [Formula: see text] as a subalgebra. Additionally, we give a representative of each representation.

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16

Nasr-Isfahani, A. R. "Hall Polynomials and Composition Algebra of Representation Finite Algebras." Algebras and Representation Theory 17, no. 4 (July 10, 2013): 1155–61. http://dx.doi.org/10.1007/s10468-013-9439-6.

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17

AdamoviĆ, Draen. "A construction of some ideals in affine vertex algebras." International Journal of Mathematics and Mathematical Sciences 2003, no. 15 (2003): 971–80. http://dx.doi.org/10.1155/s0161171203201058.

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We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of typesAandC. We find new explicit formulas for singular vectors in these vertex operator algebras at integer and half-integer levels. These formulas generalize the expressions for singular vectors from Adamović (1994). As a consequence, we obtain a new family of vertex operator algebras for which we identify the associated Zhu's algebras. A connection with the representation theory of Weyl algebras is also discussed.

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18

EHOLZER, W. "FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3495–507. http://dx.doi.org/10.1142/s0217751x93001405.

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Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

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19

Kornev, A. I., and I. P. Shestakov. "On associative representations of non-associative algebras." Journal of Algebra and Its Applications 17, no. 03 (February 5, 2018): 1850051. http://dx.doi.org/10.1142/s0219498818500512.

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We define a notion of associative representation for algebras. We prove the existence of faithful associative representations for any alternative, Mal’cev, and Poisson algebra, and prove analogs of Ado-Iwasawa theorem for each of these cases. We construct also an explicit associative representation of the Cayley–Dickson algebra in the matrix algebra [Formula: see text]

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20

Kasjan, Stanisław, and Justyna Kosakowska. "On Lie algebras associated with representation-directed algebras." Journal of Pure and Applied Algebra 214, no. 5 (May 2010): 678–88. http://dx.doi.org/10.1016/j.jpaa.2009.07.012.

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21

Di Nola, A., I. Esposito, and B. Gerla. "Local algebras in the representation of MV-algebras." Algebra universalis 56, no. 2 (March 2007): 133–64. http://dx.doi.org/10.1007/s00012-007-1984-6.

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22

Nasr-Isfahani, A. R. "On Lie algebras associated with representation-finite algebras." Journal of Algebra 444 (December 2015): 284–96. http://dx.doi.org/10.1016/j.jalgebra.2015.07.023.

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23

Zádori, László. "Relational Sets and Categorical Equivalence of Algebras." International Journal of Algebra and Computation 07, no. 05 (October 1997): 561–76. http://dx.doi.org/10.1142/s0218196797000253.

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We study relation varieties, i.e. classes of relational sets (resets) of the same type that are closed under the formation of products and retracts. The notions of an irreducible reset and a representation of a reset are defined similarly to the ones for partially ordered sets. We give a characterization of finite irreducible resets. We show that every finite reset has a representation by minimal resets which are certain distinguished irreducible retracts. It turns out that a representation by minimal resets is a smallest one in some sense among all representations of a reset. We prove that non-isomorphic finite irreducible resets generate different relation varieties. We characterize categorical equivalence of algebras via product and retract of certain resets associated with the algebras. In the finite case the characterization involves minimal resets. Examples are given to demonstrate how the general theorems work for particular algebras and resets.

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24

Chen, Fulin, Yun Gao, Naihuan Jing, and Shaobin Tan. "Twisted Vertex Operators and Unitary Lie Algebras." Canadian Journal of Mathematics 67, no. 3 (June 1, 2015): 573–96. http://dx.doi.org/10.4153/cjm-2014-010-1.

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AbstractA representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral ℤ2–lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by–product, some fundamental representations of affine Kac–Moody Lie algebra of type A(2)n are recovered by the new method.

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25

ALTSCHÜLER, D. "THE CRITICAL REPRESENTATIONS OF AFFINE LIE ALGEBRAS." Modern Physics Letters A 01, no. 10 (November 1986): 557–64. http://dx.doi.org/10.1142/s0217732386000701.

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A critical representation of an affine algebra Ĝ is a representation with central charge k=−g, g being the dual Coxeter number of the underlying simple Lie algebra G. These representations arise naturally in the study of conformal current algebras and BRS cohomology. The author shows how to construct them explicitly in a number of cases, and some intriguing open problems are mentioned.

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26

BARANOV, A. A., and A. E. ZALESSKII. "PLAIN REPRESENTATIONS OF LIE ALGEBRAS." Journal of the London Mathematical Society 63, no. 3 (June 2001): 571–91. http://dx.doi.org/10.1017/s0024610701002101.

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In this paper we study representations of finite dimensional Lie algebras. In this case representations are not necessarily completely reducible. As the general problem is known to be of enormous complexity, we restrict ourselves to representations that behave particularly well on Levi subalgebras. We call such representations plain (Definition 1.1). Informally, we show that the theory of plain representations of a given Lie algebra L is equivalent to representation theory of finitely many finite dimensional associative algebras, also non-semisimple. The sense of this is to distinguish representations of Lie algebras that are of complexity comparable with that of representations of associative algebras. Non-plain representations are intrinsically much more complex than plain ones. We view our work as a step toward understanding this complexity phenomenon.We restrict ourselves also to perfect Lie algebras L, that is, such that L = [L, L]. In our main results we assume that L is perfect and [sfr ][lfr ]2-free (which means that L has no quotient isomorphic to [sfr ][lfr ]2). The ground field [ ] is always assumed to be algebraically closed and of characteristic 0.

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27

Bui, Huu Hung. "Induced representations twisted by cocycles." Bulletin of the Australian Mathematical Society 50, no. 3 (December 1994): 399–404. http://dx.doi.org/10.1017/s0004972700013514.

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We define a notion of representation induced from cocycles which encompasses the case of Kawakami's generalised induced representation. Our purpose is to formulate Kawakami's construction within the context of Rieffel's formalism of induced representations of C*-algebras.

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28

DOTY, STEPHEN R., and DANIEL K. NAKANO. "Semisimple Schur Algebras." Mathematical Proceedings of the Cambridge Philosophical Society 124, no. 1 (July 1998): 15–20. http://dx.doi.org/10.1017/s0305004197002466.

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Schur algebras are certain finite-dimensional algebras that completely control the polynomial representation theory of the general linear groups over an infinite field. Infinitesimal Schur algebras are truncated versions of the classical Schur algebras which control the polynomial representation theory of the Frobenius kernels of general linear groups. In this paper we use some elementary results on symmetric powers to classify the semisimple Schur algebras. We then classify the semisimple infinitesimal Schur algebras as well.

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29

BANICA, TEODOR, and JULIEN BICHON. "HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS." Glasgow Mathematical Journal 52, no. 3 (August 25, 2010): 677–703. http://dx.doi.org/10.1017/s0017089510000510.

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AbstractWe develop a general theory of Hopf image of a Hopf algebra representation, with the associated concept of inner faithful representation, modelled on the notion of faithful representation of a discrete group. We study several examples, including group algebras, enveloping algebras of Lie algebras, pointed Hopf algebras, function algebras, twistings and cotwistings, and we present a Tannaka duality formulation of the notion of Hopf image.

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30

Anoussis, M., A. Katavolos, and I. G. Todorov. "Operator algebras from the discrete Heisenberg semigroup." Proceedings of the Edinburgh Mathematical Society 55, no. 1 (November 8, 2011): 1–22. http://dx.doi.org/10.1017/s0013091510000143.

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AbstractWe study reflexivity and structural properties of operator algebras generated by representations of the discrete Heisenberg semigroup. We show that the left regular representation of this semigroup gives rise to a semi-simple reflexive algebra. We exhibit an example of a representation that gives rise to a non-reflexive algebra. En route, we establish reflexivity results for subspaces of $H^{\infty}(\mathbb{T})\otimes\mathcal{B}(\mathcal{H})$.

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31

Leszczyński, Zbigniew. "Representation-tame locally hereditary algebras." Colloquium Mathematicum 99, no. 2 (2004): 175–87. http://dx.doi.org/10.4064/cm99-2-3.

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32

Skowroński, Andrzej. "Minimal representation-infinite artin algebras." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 2 (September 1994): 229–43. http://dx.doi.org/10.1017/s0305004100072546.

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Let A be an artin algebra over a commutative artin ring R, mod A be the category of finitely generated right A-modules, and rad∞ (modA) be the infinite power of the Jacobson radical rad(modA) of modA. Recall that A is said to be representation-finite if mod A admits only finitely many non-isomorphic indecomposable modules. It is known that A is representation-finite if and only if rad∞ (mod A) = 0. Moreover, from the validity of the First Brauer–Thrall Conjecture [26, 2] we know that A is representation-finite if and only if there is a common bound on the length of indecomposable modules in mod A.

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33

KOUSHESH, M. R. "REPRESENTATION THEOREMS FOR NORMED ALGEBRAS." Journal of the Australian Mathematical Society 95, no. 2 (June 17, 2013): 201–22. http://dx.doi.org/10.1017/s1446788713000207.

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AbstractWe show that for a normal locally-$\mathscr{P}$ space $X$ (where $\mathscr{P}$ is a topological property subject to some mild requirements) the subset ${C}_{\mathscr{P}} (X)$ of ${C}_{b} (X)$ consisting of those elements whose support has a neighborhood with $\mathscr{P}$, is a subalgebra of ${C}_{b} (X)$ isometrically isomorphic to ${C}_{c} (Y)$ for some unique (up to homeomorphism) locally compact Hausdorff space $Y$. The space $Y$ is explicitly constructed as a subspace of the Stone–Čech compactification $\beta X$ of $X$ and contains $X$ as a dense subspace. Under certain conditions, ${C}_{\mathscr{P}} (X)$ coincides with the set of those elements of ${C}_{b} (X)$ whose support has $\mathscr{P}$, it moreover becomes a Banach algebra, and simultaneously, $Y$ satisfies ${C}_{c} (Y)= {C}_{0} (Y)$. This includes the cases when $\mathscr{P}$ is the Lindelöf property and $X$ is either a locally compact paracompact space or a locally-$\mathscr{P}$ metrizable space. In either of the latter cases, if $X$ is non-$\mathscr{P}$, then $Y$ is nonnormal and ${C}_{\mathscr{P}} (X)$ fits properly between ${C}_{0} (X)$ and ${C}_{b} (X)$; even more, we can fit a chain of ideals of certain length between ${C}_{0} (X)$ and ${C}_{b} (X)$. The known construction of $Y$ enables us to derive a few further properties of either ${C}_{\mathscr{P}} (X)$ or $Y$. Specifically, when $\mathscr{P}$ is the Lindelöf property and $X$ is a locally-$\mathscr{P}$ metrizable space, we show that $$\begin{eqnarray*}\dim C_{\mathscr{P}}(X)= \ell \mathop{(X)}\nolimits ^{{\aleph }_{0} } ,\end{eqnarray*}$$ where $\ell (X)$ is the Lindelöf number of $X$, and when $\mathscr{P}$ is countable compactness and $X$ is a normal space, we show that $$\begin{eqnarray*}Y= {\mathrm{int} }_{\beta X} \upsilon X\end{eqnarray*}$$ where $\upsilon X$ is the Hewitt realcompactification of $X$.

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CAO, HuaiXin, ZhiHua GUO, KunLi ZHANG, and ZhengLi CHEN. "Representation theory of effect algebras." SCIENTIA SINICA Mathematica 43, no. 8 (August 1, 2013): 835–46. http://dx.doi.org/10.1360/012012-10.

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35

Koushesh, M. R. "Representation theorems for Banach algebras." Topology and its Applications 160, no. 13 (August 2013): 1781–93. http://dx.doi.org/10.1016/j.topol.2013.07.007.

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36

Abad, Manuel, J. Patricio D�az Varela, and Antoni Torrens. "Topological representation for implication algebras." algebra universalis 52, no. 1 (November 2004): 39–48. http://dx.doi.org/10.1007/s00012-004-1872-2.

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37

Pigozzi, Don, and Antonino Salibra. "Lambda abstraction algebras: representation theorems." Theoretical Computer Science 140, no. 1 (March 1995): 5–52. http://dx.doi.org/10.1016/0304-3975(94)00203-u.

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38

Oppermann, Steffen Oppermann. "Representation dimension of artin algebras." São Paulo Journal of Mathematical Sciences 4, no. 3 (December 30, 2010): 479. http://dx.doi.org/10.11606/issn.2316-9028.v4i3p479-498.

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39

Gabriel, P., and J. A. De La Peña. "Quotients of representation-finite algebras." Communications in Algebra 15, no. 1-2 (January 1987): 279–307. http://dx.doi.org/10.1080/00927878708823421.

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40

Marek Balcerzak, Artur Bartoszewicz, and Krzysztof Ciesielski. "Algebras with Inner MB-Representation." Real Analysis Exchange 29, no. 1 (2004): 265. http://dx.doi.org/10.14321/realanalexch.29.1.0265.

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41

Shen, X. R., and J. D. H. Smith. "Representation theory of comtrans algebras." Journal of Pure and Applied Algebra 80, no. 2 (July 1992): 177–95. http://dx.doi.org/10.1016/0022-4049(92)90077-s.

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42

Kim, Sangjib, and Victor Protsak. "Hibi Algebras and Representation Theory." Acta Mathematica Vietnamica 44, no. 1 (June 5, 2018): 307–23. http://dx.doi.org/10.1007/s40306-018-0263-2.

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43

Han, Shengwei, and Bin Zhao. "Representation theorems for Q-algebras." Semigroup Forum 98, no. 2 (January 29, 2019): 299–314. http://dx.doi.org/10.1007/s00233-019-10000-9.

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44

Dubuc, Eduardo J., and Yuri A. Poveda. "Representation theory of MV-algebras." Annals of Pure and Applied Logic 161, no. 8 (May 2010): 1024–46. http://dx.doi.org/10.1016/j.apal.2009.12.006.

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45

Assem, Ibrahim, and Andrzej Skowroński. "Minimal representation-infinite coil algebras." Manuscripta Mathematica 67, no. 1 (December 1990): 305–31. http://dx.doi.org/10.1007/bf02568435.

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SŁomczyńska, K. "Equivalential algebras. Part I: Representation." Algebra Universalis 35, no. 4 (December 1996): 524–47. http://dx.doi.org/10.1007/bf01243593.

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Rouquier, Raphaël. "Representation dimension of exterior algebras." Inventiones mathematicae 165, no. 2 (March 24, 2006): 357–67. http://dx.doi.org/10.1007/s00222-006-0499-7.

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Swamy, U. M., and M. K. Murthy. "Representation of fuzzy Boolean algebras." Fuzzy Sets and Systems 48, no. 2 (June 1992): 231–37. http://dx.doi.org/10.1016/0165-0114(92)90337-4.

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Barot, M. "Representation-finite derived tubular algebras." Archiv der Mathematik 74, no. 2 (February 2000): 89–94. http://dx.doi.org/10.1007/pl00000422.

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Doty, Stephen R., Karin Erdmann, Stuart Martin, and Daniel K. Nakano. "Representation type of Schur algebras." Mathematische Zeitschrift 232, no. 1 (September 1999): 137–82. http://dx.doi.org/10.1007/pl00004755.

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