Divided power (co)homology. presentations of simple finite dimensional modular lie superalgebras with cartan matrix

Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites

    Research output: Contribution to journalArticle

    Abstract

    For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we explicitly give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras with indecomposable Cartan matrix in characteristic 2 (and - in the arXiv version of the paper - in other characteristics for completeness of the picture). In the modular and super cases, we define notions of Chevalley generators and Cartan matrix, and an auxiliary notion of the Dynkin diagram. The relations of simple Lie algebras of the A, D, E types are not only Serre ones. These non-Serre relations are same for Lie superalgebras with the same Cartan matrix and any distribution of parities of the generators. Presentations of simple orthogonal Lie algebras having no Cartan matrix (indigenous for characteristic 2) are also given.

    Original languageEnglish (US)
    Pages (from-to)237-278
    Number of pages42
    JournalHomology, Homotopy and Applications
    Volume12
    Issue number1
    DOIs
    StatePublished - Jan 1 2010

    Fingerprint

    Cartan Matrix
    Lie Superalgebra
    Homology
    Generator
    Dynkin Diagram
    Simple Lie Algebra
    Parity
    Cohomology
    Completeness
    Lie Algebra
    Analogue
    Presentation

    Keywords

    • Defining relation
    • Divided power cohomology
    • Modular Lie superalgebra

    ASJC Scopus subject areas

    • Mathematics (miscellaneous)

    Cite this

    Divided power (co)homology. presentations of simple finite dimensional modular lie superalgebras with cartan matrix. / Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry.

    In: Homology, Homotopy and Applications, Vol. 12, No. 1, 01.01.2010, p. 237-278.

    Research output: Contribution to journalArticle

    Bouarroudj, Sofiane ; Grozman, Pavel ; Lebedev, Alexei ; Leites, Dimitry. / Divided power (co)homology. presentations of simple finite dimensional modular lie superalgebras with cartan matrix. In: Homology, Homotopy and Applications. 2010 ; Vol. 12, No. 1. pp. 237-278.
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