# 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

- Mathematics
- 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

- Mathematics
- 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

- MathematicsCommunications in Algebra
- 2019

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

- Mathematics
- 2005

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

- Mathematics
- 2004

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

- Mathematics
- 2015

A class of Yetter–Drinfel’d Hopf algebras on basic cycle is constructed.

Critical groups for Hopf algebra modules

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2018

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

- Mathematics
- 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…

## References

SHOWING 1-10 OF 20 REFERENCES

Ribbon graphs and their invaraints derived from quantum groups

- Mathematics
- 1990

The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum…

Irreducible representations of the quantum analogue of SU(2)

- Mathematics
- 1989

We give the complete set of irreducible representations of U(SU(2))q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not…

Quantum Groups

- Mathematics
- 1994

Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups…

Invariants of 3-manifolds via link polynomials and quantum groups

- Mathematics
- 1991

The aim of this paper is to construct new topological invariants of compact oriented 3-manifolds and of framed links in such manifolds. Our invariant of (a link in) a closed oriented 3-manifold is a…

REPRESENTATIONS AND COHOMOLOGY I: Basic representation theory of finite groups and associative algebras

- Mathematics
- 1994

Representations, duals and quantum doubles of monoidal categories

- Mathematics
- 1991

[For the entire collection see Zbl 0742.00067.]\par The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author…