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1

Chen, Xiao-yuan. "Smash product algebras over twisted dimodule algebras." Applied Mathematics-A Journal of Chinese Universities 23, no. 3 (2008): 366–70. http://dx.doi.org/10.1007/s11766-008-1919-9.

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2

Ma, Tianshui, Haiying Li, and Tao Yang. "Cobraided smash product Hom-Hopf algebras." Colloquium Mathematicum 134, no. 1 (2014): 75–92. http://dx.doi.org/10.4064/cm134-1-3.

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3

LI, HAISHENG. "A SMASH PRODUCT CONSTRUCTION OF NONLOCAL VERTEX ALGEBRAS." Communications in Contemporary Mathematics 09, no. 05 (2007): 605–37. http://dx.doi.org/10.1142/s0219199707002605.

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A notion of vertex bialgebra and a notion of nonlocal vertex module-algebra for a vertex bialgebra are studied and then a smash product construction of nonlocal vertex algebras is presented. For every nonlocal vertex algebra V satisfying a suitable condition, a canonical bialgebra B(V) is constructed such that primitive elements of B(V) are essentially pseudo-derivations and group-like elements are essentially pseudo-endomorphisms. As an application, vertex algebras associated with the Heisenberg Lie algebras as well as those associated with the nondegenerate even lattices are reconstructed th
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4

Zhou, Nan, and Shuanhong Wang. "A duality theorem for weak multiplier Hopf algebra actions." International Journal of Mathematics 28, no. 05 (2017): 1750032. http://dx.doi.org/10.1142/s0129167x1750032x.

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The main purpose of this paper is to unify the theory of actions of Hopf algebras, weak Hopf algebras and multiplier Hopf algebras to one of actions of weak multiplier Hopf algebras introduced by Van Daele and Wang. Using such developed actions, we will define the notion of a module algebra over weak multiplier Hopf algebras and construct their smash products. The main result is the duality theorem for actions and their dual actions on the smash product of weak multiplier Hopf algebras. As an application, we recover the main results found in the literature for weak Hopf algebras, multiplier Ho
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5

Ciungu, Mădălin, and Florin Panaite. "L-R-Smash Products and L-R-Twisted Tensor Products of Algebras." Algebra Colloquium 21, no. 01 (2014): 129–46. http://dx.doi.org/10.1142/s1005386714000091.

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We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance, we prove a result of the type “invariance under twisting” and we show that under certain circumstances L-R-twisted tensor products of algebras may be iterated.
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6

Cordeiro, Luiz Gustavo. "Sectional algebras of semigroupoid bundles." International Journal of Algebra and Computation 30, no. 06 (2020): 1257–304. http://dx.doi.org/10.1142/s0218196720500411.

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In this paper, we use semigroupoids to describe a notion of algebraic bundles, mostly motivated by Fell ([Formula: see text]-algebraic) bundles, and the sectional algebras associated to them. As the main motivational example, Steinberg algebras may be regarded as the sectional algebras of trivial (direct product) bundles. Several theorems which relate geometric and algebraic constructions — via the construction of a sectional algebra — are widely generalized: Direct products bundles by semigroupoids correspond to tensor products of algebras; semidirect products of bundles correspond to “naïve”
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7

Panaite, Florin, and Freddy Van Oystaeyen. "L-R-smash product for (quasi-)Hopf algebras." Journal of Algebra 309, no. 1 (2007): 168–91. http://dx.doi.org/10.1016/j.jalgebra.2006.07.020.

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8

Fang, Xiao-Li, та Tae-Hwa Kim. "(𝜃,ω)-Twisted Radford’s Hom-biproduct and ϖ-Yetter–Drinfeld modules for Hom-Hopf algebras". Journal of Algebra and Its Applications 19, № 03 (2020): 2050046. http://dx.doi.org/10.1142/s0219498820500462.

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To unify different definitions of smash Hom-products in a Hom-bialgebra [Formula: see text], we firstly introduce the notion of [Formula: see text]-twisted smash Hom-product [Formula: see text]. Secondly, we find necessary and sufficient conditions for the twisted smash Hom-product [Formula: see text] and the twisted smash Hom-coproduct [Formula: see text] to afford a Hom-bialgebra, which generalize the well-known Radford’s biproduct and the Hom-biproduct obtained in [H. Li and T. Ma, A construction of the Hom-Yetter–Drinfeld category, Colloq. Math. 137 (2014) 43–65]. Furthermore, we introduce
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9

SCHWEDE, STEFAN. "Stable homotopical algebra and Γ-spaces". Mathematical Proceedings of the Cambridge Philosophical Society 126, № 2 (1999): 329–56. http://dx.doi.org/10.1017/s0305004198003272.

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In this paper we advertise the category of Γ-spaces as a convenient framework for doing ‘algebra’ over ‘rings’ in stable homotopy theory. Γ-spaces were introduced by Segal [Se] who showed that they give rise to a homotopy category equivalent to the usual homotopy category of connective (i.e. (−1)-connected) spectra. Bousfield and Friedlander [BF] later provided model category structures for Γ-spaces. The study of ‘rings, modules and algebras’ based on Γ-spaces became possible when Lydakis [Ly] introduced a symmetric monoidal smash product with good homotopical properties. Here we develop model
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10

Borges, Inês, and Christian Lomp. "Quantum Groupoids Acting on Semiprime Algebras." Advances in Mathematical Physics 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/546058.

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11

Wang, Hao. "Hopf actions on vertex operator algebras, II: Smash product." Journal of Algebra 530 (July 2019): 402–28. http://dx.doi.org/10.1016/j.jalgebra.2019.04.018.

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12

MAKHLOUF, ABDENACER, and FLORIN PANAITE. "TWISTING OPERATORS, TWISTED TENSOR PRODUCTS AND SMASH PRODUCTS FOR HOM-ASSOCIATIVE ALGEBRAS." Glasgow Mathematical Journal 58, no. 3 (2015): 513–38. http://dx.doi.org/10.1017/s0017089515000294.

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AbstractThe purpose of this paper is to provide new constructions of Hom-associative algebras using Hom-analogues of certain operators called twistors and pseudotwistors, by deforming a given Hom-associative multiplication into a new Hom-associative multiplication. As examples, we introduce Hom-analogues of the twisted tensor product and smash product. Furthermore, we show that the construction by the twisting principle introduced by Yau and the twisting of associative algebras using pseudotwistors admit a common generalization.
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13

Mira, José Antonio Cuenca. "On structure theory of pre-Hilbert algebras." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 2 (2009): 303–19. http://dx.doi.org/10.1017/s0308210507000753.

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Let A be a real (non-associative) algebra which is normed as real vector space, with a norm ‖·‖ deriving from an inner product and satisfying ‖ac‖ ≤ ‖a‖‖c‖ for any a,c ∈ A. We prove that if the algebraic identity (a((ac)a))a = (a2c)a2 holds in A, then the existence of an idempotent e such that ‖e‖ = 1 and ‖ea‖ = ‖a‖ = ‖ae‖, a ∈ A, implies that A is isometrically isomorphic to ℝ, ℂ, ℍ, $\mathbb{O}$,\, $\stackrel{\raisebox{4.5pt}[0pt][0pt]{\fontsize{4pt}{4pt}\selectfont$\star$}}{\smash{\CC}}$,\, $\stackrel{\raisebox{4.5pt}[0pt][0pt]{\fontsize{4pt}{4pt}\selectfont$\star$}}{\smash{\mathbb{H}}}$,\,
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14

Ma, Tianshui, Linlin Liu, and Shaoxian Xu. "Twisted tensor biproduct monoidal Hom–Hopf algebras." Asian-European Journal of Mathematics 10, no. 01 (2017): 1750011. http://dx.doi.org/10.1142/s1793557117500115.

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Let [Formula: see text] be a monoidal Hom-bialgebra, [Formula: see text] a monoidal Hom-algebra and a monoidal Hom-coalgebra. Let [Formula: see text] and [Formula: see text] be two linear maps. First, we construct the [Formula: see text]-smash product monoidal Hom-algebra [Formula: see text] and [Formula: see text]-smash coproduct monoidal Hom-coalgebra [Formula: see text]. Second, the necessary and sufficient conditions for [Formula: see text] and [Formula: see text] to be a monoidal Hom-bialgebra are obtained, which generalizes the results in [8, 11]. Lastly, we give some examples and applic
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15

Panaite, Florin. "Iterated crossed products." Journal of Algebra and Its Applications 13, no. 07 (2014): 1450036. http://dx.doi.org/10.1142/s0219498814500364.

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We define a "mirror version" of Brzeziński's crossed product and we prove that, under certain circumstances, a Brzeziński crossed product D ⊗R,σ V and a mirror version [Formula: see text] may be iterated, obtaining an algebra structure on W ⊗ D ⊗ V. Particular cases of this construction are the iterated twisted tensor product of algebras and the quasi-Hopf two-sided smash product.
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16

Walton, Chelsea, and Sarah Witherspoon. "Poincaré–Birkhoff–Witt deformations of smash product algebras from Hopf actions on Koszul algebras." Algebra & Number Theory 8, no. 7 (2014): 1701–31. http://dx.doi.org/10.2140/ant.2014.8.1701.

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17

Jiao, Zhengming. "The quasitriangular structures for a class ofT-smash product Hopf algebras." Israel Journal of Mathematics 146, no. 1 (2005): 125–47. http://dx.doi.org/10.1007/bf02773530.

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18

Yan, Yan, Cui Lan Mi, and Xin Chun Wang. "Relations of A*H and AH." Advanced Materials Research 143-144 (October 2010): 828–31. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.828.

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In this paper, we study the concept of the right twisted smash product algebra A*H over weak Hopf algebra. Let H be a weak Hopf algebra and A an H-module algebra, using the properties of the trace function we describe the finiteness conditions for H-module algebras.
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19

WISBAUER, ROBERT. "LIFTING THEOREMS FOR TENSOR FUNCTORS ON MODULE CATEGORIES." Journal of Algebra and Its Applications 10, no. 01 (2011): 129–55. http://dx.doi.org/10.1142/s0219498811004471.

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Any (co)ring R is an endofunctor with (co)multiplication on the category of abelian groups. These notions were generalized to monads and comonads on arbitrary categories. Starting around 1970 with papers by Beck, Barr and others a rich theory of the interplay between such endofunctors was elaborated based on distributive laws between them and Applegate's lifting theorem of functors between categories to related (co)module categories. Curiously enough some of these results were not noticed by researchers in module theory and thus notions like entwining structures and smash products between alge
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20

Castro, Felipe, Antonio Paques, Glauber Quadros, and Alveri Sant'Ana. "Partial actions of weak Hopf algebras: Smash product, globalization and Morita theory." Journal of Pure and Applied Algebra 219, no. 12 (2015): 5511–38. http://dx.doi.org/10.1016/j.jpaa.2015.05.031.

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21

Bagio, Dirceu, Daiana Flôres, and Alveri Sant’ana. "Inner actions of weak Hopf algebras." Journal of Algebra and Its Applications 16, no. 06 (2017): 1750118. http://dx.doi.org/10.1142/s0219498817501183.

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Let [Formula: see text] be an associative ring and [Formula: see text] idempotent elements of [Formula: see text]. In this paper we introduce the notion of [Formula: see text]-invertibility for an element of [Formula: see text] and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra [Formula: see text] and an algebra [Formula: see text], we present sufficient conditions for [Formula: see text] to admit an inner action of [Formula: see text]. We also prove that if [Formula: see text] is a left [Formula: see text]-module algebra then [Formula: see text] acts innerly o
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22

Liangyun, Zhang, and Zhu Shenglin. "Fundamental Theorems of Weak Doi–Hopf Modules and Semisimple Weak Smash Product Hopf Algebras." Communications in Algebra 32, no. 9 (2004): 3403–15. http://dx.doi.org/10.1081/agb-120039396.

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23

WANG, YONG, and GUANGQUAN GUO. "SMASH PRODUCTS, SEPARABLE EXTENSIONS AND A MORITA CONTEXT OVER HOPF ALGEBROIDS." Journal of Algebra and Its Applications 13, no. 04 (2014): 1350124. http://dx.doi.org/10.1142/s0219498813501247.

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Let [Formula: see text] be a Hopf algebroid, and A a left [Formula: see text]-module algebra. This paper is concerned with the smash product algebra A#H over Hopf algebroids. In this paper, we investigate separable extensions for module algebras over Hopf algebroids. As an application, we obtain a Maschke-type theorem for A#H-modules over Hopf algebroids, which generalizes the corresponding result given by Cohen and Fischman in [Hopf algebra actions, J. Algebra100 (1986) 363–379]. Furthermore, based on the work of Kadison and Szlachányi in [Bialgebroid actions on depth two extensions and duali
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24

Poinsot, Laurent. "Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category." Algebra 2013 (September 19, 2013): 1–10. http://dx.doi.org/10.1155/2013/370618.

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A locally finite category is defined as a category in which every arrow admits only finitely many different ways to be factorized by composable arrows. The large algebra of such categories over some fields may be defined, and with it a group of invertible series (under multiplication). For certain particular locally finite categories, a substitution operation, generalizing the usual substitution of formal power series, may be defined, and with it a group of reversible series (invertible under substitution). Moreover, both groups are actually affine groups. In this contribution, we introduce th
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25

Beattie, Margaret. "Automorphisms of G-Azumaya Algebras." Canadian Journal of Mathematics 37, no. 6 (1985): 1047–58. http://dx.doi.org/10.4153/cjm-1985-056-7.

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Let R be a commutative ring, G a finite abelian group of order n and exponent m, and assume n is a unit in R. In [10], F. W. Long defined a generalized Brauer group, BD(R, G), of algebras with a G-action and G-grading, whose elements are equivalence classes of G-Azumaya algebras. In this paper we investigate the automorphisms of a G-Azumaya algebra A and prove that if Picm(R) is trivial, then these automorphisms are all, in some sense, inner.In fact, each of these “inner” automorphisms can be written as the composition of an inner automorphism in the usual sense and a “linear“ automorphism, i.
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26

Wang, Caihong, and Shenglin Zhu. "Smash Products ofH-Simple Module Algebras." Communications in Algebra 41, no. 5 (2013): 1836–45. http://dx.doi.org/10.1080/00927872.2011.651761.

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27

Qingzhong, Ji, and Qin Hourong. "On Smash Products Of Hopf Algebras." Communications in Algebra 34, no. 9 (2006): 3203–22. http://dx.doi.org/10.1080/00927870600778365.

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28

Wang, Wei, Nan Zhou, and Shuanhong Wang. "Semidirect products of weak multiplier Hopf algebras: Smash products and smash coproducts." Communications in Algebra 46, no. 8 (2018): 3241–61. http://dx.doi.org/10.1080/00927872.2017.1407421.

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29

Jia, Ling. "The structure theorem and duality theorem for endomorphism algebras of weak Hopf group coalgebras." Journal of Algebra and Its Applications 16, no. 11 (2017): 1750208. http://dx.doi.org/10.1142/s0219498817502085.

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In this paper, we investigate the HOM-functor and state the structure theorem for endomorphism algebras of weak two-sided [Formula: see text]-Hopf [Formula: see text]-modules in order to explore homological algebras for weak Hopf [Formula: see text]-modules, and present the duality theorem for weak group “big” Smash products which extends the result of Menini and Raianu [Morphisms of relative Hopf modules, Smash products and duality, J. Algebra 219 (1999) 547–570] in the setting of weak Hopf group coalgebras.
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30

Le Meur, Patrick. "Smash products of Calabi–Yau algebras by Hopf algebras." Journal of Noncommutative Geometry 13, no. 3 (2019): 887–961. http://dx.doi.org/10.4171/jncg/341.

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31

Liangyun, Zhang. "L-R smash products for bimodule algebras*." Progress in Natural Science 16, no. 6 (2006): 580–87. http://dx.doi.org/10.1080/10020070612330038.

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32

Childs, L. N. "Azumaya algebras which are not smash products." Rocky Mountain Journal of Mathematics 20, no. 1 (1990): 75–89. http://dx.doi.org/10.1216/rmjm/1181073160.

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33

Zhu, Bin. "Smash products of quasi-hereditary graded algebras." Archiv der Mathematik 72, no. 6 (1999): 433–37. http://dx.doi.org/10.1007/s000130050352.

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34

Wang, Caihong, and Shenglin Zhu. "On smash products of transitive module algebras." Chinese Annals of Mathematics, Series B 31, no. 4 (2010): 541–54. http://dx.doi.org/10.1007/s11401-010-0586-3.

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35

Zhang, Liangyun, Huixiang Chen, and Jinqi Li. "TWISTED PRODUCTS AND SMASH PRODUCTS OVER WEAK HOPF ALGEBRAS." Acta Mathematica Scientia 24, no. 2 (2004): 247–58. http://dx.doi.org/10.1016/s0252-9602(17)30381-8.

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36

Delvaux, Lydia. "SEMI-DIRECT PRODUCTS OF MULTIPLIER HOPF ALGEBRAS: SMASH PRODUCTS." Communications in Algebra 30, no. 12 (2002): 5961–77. http://dx.doi.org/10.1081/agb-120016026.

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37

Liu, Wei, Xiaoli Fang, and Blas Torrecillas. "Twisted BiHom-smash products and L-R BiHom-smash products for monoidal BiHom-Hopf algebras." Colloquium Mathematicum 159, no. 2 (2020): 171–93. http://dx.doi.org/10.4064/cm7695-12-2018.

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38

Bergen, Jeffrey. "A note on smash products over frobenius algebras." Communications in Algebra 21, no. 11 (1993): 4021–24. http://dx.doi.org/10.1080/00927879308824780.

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39

Pan, Qun-xing. "On L-R Smash Products of Hopf Algebras." Communications in Algebra 40, no. 10 (2012): 3955–73. http://dx.doi.org/10.1080/00927872.2011.576735.

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40

Pirkovskii, A. Yu. "Arens-Michael enveloping algebras and analytic smash products." Proceedings of the American Mathematical Society 134, no. 9 (2006): 2621–31. http://dx.doi.org/10.1090/s0002-9939-06-08251-7.

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41

Zhao, Li-hui, Di-Ming Lu, and Xiao-li Fang. "L-R smash products for multiplier Hopf algebras." Applied Mathematics-A Journal of Chinese Universities 23, no. 1 (2008): 83–90. http://dx.doi.org/10.1007/s11766-008-0112-5.

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42

Bulacu, Daniel, Florin Panaite, and Freddy Van Oystaeyen. "Quasi-hopf algebra actions and smash products." Communications in Algebra 28, no. 2 (2000): 631–51. http://dx.doi.org/10.1080/00927870008826849.

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43

Koppinen, M. "Coideal subalgebras in hopf algebras: freeness, integrals, smash products." Communications in Algebra 21, no. 2 (1993): 427–44. http://dx.doi.org/10.1080/00927879308824572.

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44

Yang, Shilin, and Zhixi Wang. "The semisimplicity of smash products of quantum commutative algebras." Communications in Algebra 27, no. 3 (1999): 1165–70. http://dx.doi.org/10.1080/00927879908826487.

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45

Liu, Ling, and Qiao-ling Guo. "On Twisted Smash Products of Monoidal Hom–Hopf Algebras." Communications in Algebra 44, no. 10 (2016): 4140–64. http://dx.doi.org/10.1080/00927872.2015.1087003.

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46

Delvaux, Lydia. "SEMI-DIRECT PRODUCTS OF MULTIPLIER HOPF ALGEBRAS: SMASH COPRODUCTS." Communications in Algebra 30, no. 12 (2002): 5979–97. http://dx.doi.org/10.1081/agb-120016027.

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47

Dăscălescu, S., C. Năstăsescu, and L. Năstăsescu. "Symmetric algebras in categories of corepresentations and smash products." Journal of Algebra 465 (November 2016): 62–80. http://dx.doi.org/10.1016/j.jalgebra.2016.07.012.

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48

Gaddis, Jason, Robert Won, and Daniel Yee. "Discriminants of Taft Algebra Smash Products and Applications." Algebras and Representation Theory 22, no. 4 (2018): 785–99. http://dx.doi.org/10.1007/s10468-018-9798-0.

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49

Bulacu, Daniel, Florin Panaite, and Freddy Van Oystaeyen. "Generalized Diagonal Crossed Products and Smash Products for Quasi-Hopf Algebras. Applications." Communications in Mathematical Physics 266, no. 2 (2006): 355–99. http://dx.doi.org/10.1007/s00220-006-0051-z.

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50

Johnson, Garrett, and Christopher Nowlin. "The FRT-construction via quantum affine algebras and smash products." Journal of Algebra 353, no. 1 (2012): 158–73. http://dx.doi.org/10.1016/j.jalgebra.2011.12.006.

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