Pavel Grozman

  1. Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix.

    Authors: Sofiane Bouarroudj, Alexei Lebedev, Pavel Grozman, Dimitry Leites
    Subjects: Representation Theory
    Abstract

    For modular Lie superalgebras, new notions are introduced: Divided power
    homology and divided power cohomology. For illustration, we give presentations
    (in terms of analogs of Chevalley generators) of finite dimensional Lie
    (super)algebras with indecomposable Cartan matrix in characteristic 2 (and in
    other characteristics for completeness of the picture).

    We correct the currently available in the literature notions of Chevalley
    generators and Cartan matrix in the modular and super cases, and an auxiliary
    notion of the Dynkin diagram.

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