Relevant bibliographies by topics / Commutative algebra. Algebras, Linear. Transformations (Mathematics) Linear transformations

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Academic literature on the topic 'Commutative algebra. Algebras, Linear. Transformations (Mathematics) Linear transformations'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Commutative algebra. Algebras, Linear. Transformations (Mathematics) Linear transformations"

1

Domokos, Mátyás, and Vesselin Drensky. "Rationality of Hilbert series in noncommutative invariant theory." International Journal of Algebra and Computation 27, no. 07 (2017): 831–48. http://dx.doi.org/10.1142/s0218196717500394.

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It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has a rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.
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2

Blute, R. F., and P. J. Scott. "The shuffle Hopf algebra and noncommutative full completeness." Journal of Symbolic Logic 63, no. 4 (1998): 1413–36. http://dx.doi.org/10.2307/2586659.

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AbstractWe present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffle algebra Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces.This paper is a natural extension of the authors' previous work, “Linear Läuchli Semantics”, where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals.
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3

Rebei, Habib, Luigi Accardi, and Hajer Taouil. "Tensor Bogolyubov representations of the renormalized square of white noise (RSWN) algebra." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 04 (2019): 1950025. http://dx.doi.org/10.1142/s0219025719500255.

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We introduce the quadratic analog of the tensor Bogolyubov representation of the CCR. Our main result is the determination of the structure of these maps: each of them is uniquely determined by two arbitrary complex-valued Borel functions of modulus [Formula: see text] and two maps of [Formula: see text] into itself whose inverses induce transformations that map the Lebesgue measure [Formula: see text] into measures [Formula: see text] absolutely continuous with respect to it. Furthermore, the Radon–Nikodyn derivatives [Formula: see text], of these measures with respect to [Formula: see text], must satisfy the relation [Formula: see text] for [Formula: see text]-almost every [Formula: see text]. This makes a surprising bridge with the hyperbolic sine and cosine defining the structure of usual (i.e. first-order) Bogolyubov transformations. The reason of the surprise is that the linear and quadratic commutation relations are completely different.
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4

Boasso, Enrico. "Joint spectra and nilpotent lie algebras of linear transformations." Linear Algebra and its Applications 263 (September 1997): 49–62. http://dx.doi.org/10.1016/s0024-3795(96)00481-8.

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5

Aceves, Kelly, and Manfred Dugas. "Local multiplication maps on F[x]." Journal of Algebra and Its Applications 14, no. 03 (2014): 1550029. http://dx.doi.org/10.1142/s0219498815500292.

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Let F be a field and A a F-algebra. The F-linear transformation φ : A → A is a local multiplication map if for all a ∈ A there exists some ua ∈ A such that φ(a) = aua. Let [Formula: see text] denote the F-algebra of all local multiplication maps of A. If F is infinite and F[x] is the ring of polynomials over F, then it is known Lemma 1 in [J. Buckner and M. Dugas, Quasi-Localizations of ℤ, Israel J. Math.160 (2007) 349–370] that [Formula: see text]. The purpose of this paper is to study [Formula: see text] for finite fields F. It turns out that in this case [Formula: see text] is a "very" non-commutative ring of cardinality 2ℵ0 with many interesting properties.
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6

Jeyaraman, I., and V. Vetrivel. "Jordan quadratic SSM-property and its relation to copositive linear transformations on Euclidean Jordan algebras." Linear Algebra and its Applications 433, no. 2 (2010): 390–400. http://dx.doi.org/10.1016/j.laa.2010.03.005.

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7

Dean, Samuel. "Duality and contravariant functors in the representation theory of artin algebras." Journal of Algebra and Its Applications 18, no. 06 (2019): 1950111. http://dx.doi.org/10.1142/s0219498819501111.

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We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring [Formula: see text] as the kernels of certain functors [Formula: see text] rather than of functors [Formula: see text] which are given by a pp-pair. This paper will give various algebraic characterizations of these functors in the case that [Formula: see text] is an artin algebra. Suppose that [Formula: see text] is an artin algebra. An additive functor [Formula: see text] preserves inverse limits and [Formula: see text] is finitely presented if and only if there is a sequence of natural transformations [Formula: see text] for some [Formula: see text] which is exact when evaluated at any left [Formula: see text]-module. Any additive functor [Formula: see text] with one of these equivalent properties has a definable kernel, and every definable subcategory of [Formula: see text] can be obtained as the kernel of a family of such functors. In the final section, a generalized setting is introduced, so that our results apply to more categories than those of the form [Formula: see text] for an artin algebra [Formula: see text]. That is, our results are extended to those locally finitely presented [Formula: see text]-linear categories whose finitely presented objects form a dualizing variety, where [Formula: see text] is a commutative artinian ring.
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8

Nikonov, V. I. "The application of Lie algebras and groups to the solution of problems of partial stability of dynamical systems." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 3 (2018): 295–303. http://dx.doi.org/10.15507/2079-6900.20.201802.295-303.

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The article is devoted to the analysis of partial stability of nonlinear systems of ordinary differential equations using Lie algebras and groups. It is shown that the existence of a group of transformations invariant under partial stability in the system under study makes it possible to simplify the analysis of the partial stability of the initial system. For this it is necessary that the associated linear differential operator Lie in the enveloping Lie algebra of the original system, and the operator defined by the one-parameter Lie group is commutative with this operator. In this case, if the found group has invariance with respect to partial stability, then the resulting transformation performs to the decomposition of the system under study, and the partial stability problem reduces to the investigation of the selected subsystem. Finding the desired transformation uses the first integrals of the original system. Examples illustrating the proposed approach are given.
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9

Nikonov, Vladimir I. "The application of Lie algebras and groups to the solution of problems of partial stability of dynamical systems." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 3 (2018): 295–303. http://dx.doi.org/10.15507/2079-6900.20.201803.295-303.

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The article is devoted to the analysis of partial stability of nonlinear systems of ordinary differential equations using Lie algebras and groups. It is shown that the existence of a group of transformations invariant under partial stability in the system under study makes it possible to simplify the analysis of the partial stability of the initial system. For this it is necessary that the associated linear differential operator Lie in the enveloping Lie algebra of the original system, and the operator defined by the one-parameter Lie group is commutative with this operator. In this case, if the found group has invariance with respect to partial stability, then the resulting transformation performs to the decomposition of the system under study, and the partial stability problem reduces to the investigation of the selected subsystem. Finding the desired transformation uses the first integrals of the original system. Examples illustrating the proposed approach are given.
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10

Denecke, Klaus. "Partial clones." Asian-European Journal of Mathematics 13, no. 08 (2020): 2050161. http://dx.doi.org/10.1142/s1793557120501612.

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A set [Formula: see text] of operations defined on a nonempty set [Formula: see text] is said to be a clone if [Formula: see text] is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the [Formula: see text]-ary operations defined on set [Formula: see text] for all natural numbers [Formula: see text] and the operations are the so-called superposition operations [Formula: see text] for natural numbers [Formula: see text] and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set [Formula: see text] and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.
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Books on the topic "Commutative algebra. Algebras, Linear. Transformations (Mathematics) Linear transformations"

1

Linear algebra and projective geometry. Dover Publications, 2005.

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2

Conceição, Carvalho, ed. Beginning with linear algebra. 2nd ed. W.H. Freeman, 2005.

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3

Transform Linear Algebra. Prentice Hall, 2001.

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Uhlig, Frank. Transform Linear Algebra. Prentice Hall, 2001.

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5

Carlen, Eric, and Carlen Loss. Linear Algebra for a Calculus Curriculum Prelim Ed. W.H. Freeman & Company, 2002.

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Discrete Fourier and Wavelet Transforms: An Introduction Through Linear Algebra with Applications to Signal Processing. World Scientific Publishing Co Pte Ltd, 2016.

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