A quiver quantum group
@article{Cibils1993AQQ, title={A quiver quantum group}, author={Claude Cibils}, journal={Communications in Mathematical Physics}, year={1993}, volume={157}, pages={459-477} }
We construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dimensional associative algebras.
81 Citations
Duality Between Quantum Symmetric Algebras
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- 2005
Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.
Hochschild and cyclic homology of a family of Auslander algebras
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- 2002
In this paper, we compute the Hochschild and cyclic homologies of the Auslander algebras of the Taft algebras. We also describe the first Chern character for the Taft algebras and for their Auslander…
Representations of the small nonstandard quantum groups
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Abstract In this paper, we study the representations of a class of small nonstandard quantum group over which the isomorphism classes of all indecomposable modules are classified, and the…
Graded Hopf algebras and pairings
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We study positively-graded Hopf algebras and obtain (dual) Gabriel-type results on graded Hopf algebras. Using it, we get certain (non-degenerate) graded Hopf pairings between quantum symmetric…
Construct bi-Frobenius algebras via quivers
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The aim of this note is to construct explicitly a class of bi-Frobenius algebras via quivers. In particular, this kind of bi-Frobenius algebras are not Hopf algebras, and a necessary and sufficient…
Yetter–Drinfel’d Hopf Algebras on Basic Cycle
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A class of Yetter–Drinfel’d Hopf algebras on basic cycle is constructed.
Critical groups for Hopf algebra modules
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Abstract This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalises the critical groups of complex finite group representations…
Quivers, Quasi-Quantum Groups and Finite Tensor Categories
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- 2011
We study finite quasi-quantum groups in their quiver setting developed recently by the first author. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation…
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