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

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 W...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 197; no. 1; pp. 139 - 187
Main Authors Heckenberger, István, Schneider, Hans-Jürgen
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.10.2013
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Hilbert Series
Drinfeld Module
Quantum Group
Hopf Algebra
Weyl Group
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-012-0180-3