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

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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.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., D-35032, Marburg, Germany

    István Heckenberger

  2. Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, Munich, Germany

    Hans-Jürgen Schneider

Authors
  1. István Heckenberger
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  2. Hans-Jürgen Schneider
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Correspondence to István Heckenberger.

Additional information

The work of I.H. is supported by DFG by a Heisenberg fellowship.

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Heckenberger, I., Schneider, HJ. Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid. Isr. J. Math. 197, 139–187 (2013). https://doi.org/10.1007/s11856-012-0180-3

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  • DOI: https://doi.org/10.1007/s11856-012-0180-3

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