The Nichols algebra of a semisimple Yetter-Drinfeld module

Details The Nichols algebra of a semisimple Yetter-Drinfeld module The Nichols algebra of a semisimple Yetter-Drinfeld module

2008-03-17

arxiv.org/abs/0803.2430v2

Mathematics

Quantum Algebra

54 pages

Scientific paper

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

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