Pointed Hopf Algebras with classical Weyl Groups

Shouchuan Zhang; Yao-Zhong Zhang

doi:10.1142/S0129167X12500668

Pointed Hopf Algebras with classical Weyl Groups

Quantum Algebra 2012-05-03 v3

Authors: Shouchuan Zhang , Yao-Zhong Zhang

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Abstract

We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups $A \rtimes \mathbb S_n$ supported by $\mathbb S_n$ are infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups $A \rtimes \mathbb S_n$ supported by $A$ to be finite dimensional.

Keywords

hopf algebras representation theory of algebras weyl groups and algebras

Cite

@article{arxiv.0910.1280,
  title  = {Pointed Hopf Algebras with classical Weyl Groups},
  author = {Shouchuan Zhang and Yao-Zhong Zhang},
  journal= {arXiv preprint arXiv:0910.1280},
  year   = {2012}
}

Comments

Combined with arXiv:0902.4748 plus substantial changes. To appear International Journal of Mathematics

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