Finite dimensional Nichols algebras over finite cyclic groups

Weicai Wu; Shouchuan Zhang; Yao-Zhong Zhang

Finite dimensional Nichols algebras over finite cyclic groups

Number Theory 2013-10-10 v3

Authors: Weicai Wu , Shouchuan Zhang , Yao-Zhong Zhang

Abstract

All finite dimensional Nichols algebras with diagonal type of connected finite dimensional Yetter-Drinfeld modules over finite cyclic group $\mathbb Z_n$ are found. It is proved that finite dimensional Nichols algebra over $\mathbb Z_2$ is a quantum linear space and Nichols algebra of connected Yetter-Drinfeld module $V$ over $\mathbb Z_n$ with $\dim V >3$ is infinite dimensional.

Keywords

finite-dimensional algebras algebra classification and gradings representation theory of algebras

Cite

@article{arxiv.1201.2064,
  title  = {Finite dimensional Nichols algebras over finite cyclic groups},
  author = {Weicai Wu and Shouchuan Zhang and Yao-Zhong Zhang},
  journal= {arXiv preprint arXiv:1201.2064},
  year   = {2013}
}

Comments

22 pages, substantially shortened and reference added. Version to appear in Journal of Lie Theory

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