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

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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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