English

The Nichols algebra of a semisimple Yetter-Drinfeld module

Quantum Algebra 2009-02-04 v2

Abstract

We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a `reflection' in the class of such Nichols algebras. We conclude the classifications of finite-dimensional pointed Hopf algebras over S_3, and of finite-dimensional Nichols algebras over S_4. The revised version contains an extended introduction with references to recent applications, and a simplified definition of the Weyl groupoid of a semisimple Yetter-Drinfeld module. Key words: Hopf algebras, quantum groups, Weyl groupoid

Keywords

Cite

@article{arxiv.0803.2430,
  title  = {The Nichols algebra of a semisimple Yetter-Drinfeld module},
  author = {N. Andruskiewitsch and I. Heckenberger and H. -J. Schneider},
  journal= {arXiv preprint arXiv:0803.2430},
  year   = {2009}
}

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54 pages