Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid.

Authors: I. Heckenberger, H.-J. Schneider
Subjects: Quantum Algebra

link: http://arxiv.org/abs/0909.0293
Abstract

We study graded right coideal subalgebras of Nichols algebras of semisimple
Yetter-Drinfeld modules. Assuming that the Yetter-Drinfeld module admits all
reflections and the Nichols algebra is decomposable, we construct an injective
order preserving and order reflecting map between morphisms of the Weyl
groupoid and graded right coideal subalgebras of the Nichols algebra. Here
morphisms are ordered with respect to right Duflo order and right coideal
subalgebras are ordered with respect to inclusion. If the Weyl groupoid is
finite, then we prove that the Nichols algebra is decomposable and the above
map is bijective. In the special case of the Borel part of quantized enveloping
algebras our result implies a conjecture of Kharchenko.

Key words: Hopf algebra, quantum group, root system, Weyl group

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