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I. Heckenberger

  1. Finite Weyl groupoids of rank three.

    Wed, 12/02/2009 - 16:01 — SomNambul
    Authors: I. Heckenberger, M. Cuntz
    Subjects: Group Theory
    Abstract

    We continue our study of Cartan schemes and their Weyl groupoids. The results
    in this paper provide an algorithm to determine connected simply connected
    Cartan schemes of rank three, where the real roots form a finite irreducible
    root system. The algorithm terminates: Up to equivalence there are exactly 55
    such Cartan schemes, and the number of corresponding real roots varies between
    6 and 37. We identify those Weyl groupoids which appear in the classification
    of Nichols algebras of diagonal type.

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

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: I. Heckenberger, H.-J. Schneider
    Subjects: Quantum Algebra
    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.

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