Root systems and Weyl groupoids for Nichols algebras

Details Root systems and Weyl groupoids for Nichols algebras Root systems and Weyl groupoids for Nichols algebras

2008-07-04

arxiv.org/abs/0807.0691v1

Mathematics

Quantum Algebra

40 pages

Scientific paper

Motivated by work of Kac and Lusztig, we define a root system and a Weyl groupoid for a large class of semisimple Yetter-Drinfeld modules over an arbitrary Hopf algebra. The obtained combinatorial structure fits perfectly into an existing framework of generalized root systems associated to a family of Cartan matrices, and provides novel insight into Nichols algebras. We demonstrate the power of our construction with new results on Nichols algebras over finite non-abelian simple groups and symmetric groups. Key words: Hopf algebra, quantum group, root system, Weyl group

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