Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form

Saïd Benayadi, Sofiane Bouarroudj

    Research output: Contribution to journalArticle

    Abstract

    A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result of simultaneously adding to it a central element and an outer derivation so that the larger algebra has also a NIS. Affine loop algebras, Lie (super)algebras with symmetrizable Cartan matrix over any field, Manin triples, symplectic reflection (super)algebras are among the Lie (super)algebras suitable to be doubly extended. We consider double extensions of Lie superalgebras in characteristic 2, and concentrate on peculiarities of these notions related with the possibility for the bilinear form, the center, and the derivation to be odd. Two Lie superalgebras we discovered by this method are indigenous to the characteristic 2.

    Original languageEnglish (US)
    Pages (from-to)141-179
    Number of pages39
    JournalJournal of Algebra
    Volume510
    DOIs
    StatePublished - Sep 15 2018

    Fingerprint

    Lie Superalgebra
    Bilinear form
    Invariant
    Cartan Matrix
    Central Element
    Loop Algebra
    Superalgebra
    Odd
    Algebra

    Keywords

    • Characteristic 2
    • Double extension
    • Lie superalgebra

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form. / Benayadi, Saïd; Bouarroudj, Sofiane.

    In: Journal of Algebra, Vol. 510, 15.09.2018, p. 141-179.

    Research output: Contribution to journalArticle

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