The category of partial Doi-Hopf modules and functors
Q.-G. Chen, D.-G. Wang (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Q.-G. Chen, D.-G. Wang (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2016)
Colloquium Mathematicae
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We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.
Roberto Martínez-Villa, Manuel Saorín (2005)
Colloquium Mathematicae
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The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.
Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2014)
Colloquium Mathematicae
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A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category . Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.
R. James Shank (1992)
Mathematische Zeitschrift
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Guillaume Tomasini (2013)
Annales de l’institut Fourier
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The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple. ...
Shuangjian Guo, Xiaohui Zhang (2016)
Colloquium Mathematicae
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Let be the category of Doi Hom-Hopf modules, be the category of A-Hom-modules, and F be the forgetful functor from to . The aim of this paper is to give a necessary and suffcient condition for F to be separable. This leads to a generalized notion of integral. Finally, applications of our results are given. In particular, we prove a Maschke type theorem for Doi Hom-Hopf modules.
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang (2016)
Colloquium Mathematicae
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We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of...
Costel-Gabriel Bontea (2014)
Czechoslovak Mathematical Journal
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We continue the study started recently by Agore, Bontea and Militaru in “Classifying bicrossed products of Hopf algebras” (2014), by describing and classifying all Hopf algebras that factorize through two Sweedler’s Hopf algebras. Equivalently, we classify all bicrossed products . There are three steps in our approach. First, we explicitly describe the set of all matched pairs by proving that, with the exception of the trivial pair, this set is parameterized by the ground field...
Shuangjian Guo, Xiu-Li Chen (2014)
Czechoslovak Mathematical Journal
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Let be a monoidal Hom-Hopf algebra and a right -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor from the category of relative Hom-Hopf modules to the category of right -Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the -coaction to be separable. This leads...
K. Erdmann, D. Madsen, V. Miemietz (2010)
Colloquium Mathematicae
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We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
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Andrzej Tyc (1998)
Colloquium Mathematicae
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Tianshui Ma, Haiying Li, Tao Yang (2014)
Colloquium Mathematicae
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Let (A,α) and (B,β) be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: R-smash products . Moreover, necessary and sufficient conditions for to be a cobraided Hom-Hopf algebra are given.
José N. Alonso Alvarez, José Manuel Fernández Vilaboa, Ramón González Rodríguez (2001)
Publicacions Matemàtiques
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Let τ be an invertible skew pairing on (B,H) where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category γD and there exists a Hopf algebra isomorphism w: B ∞ H → B [×] H in C, where B ∞ H is a Hopf algebra with (co)algebra structure the smash (co)product and B [×] H is the Hopf algebra defined by Doi and Takeuchi. ...