On Degenerations of Lie Superalgebras

2018/02/23 by María Alejandra Alvarez, Isabel Hernández, Alvarez, María Alejandra +1
Mathematics · #17B30 #17B56 #17B99 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B30 #msc:17B56 #msc:17B99

paper · pdf · doi:10.48550/arxiv.1802.08707

12 pages

arxiv created 2018/02/23 · arxiv updated 2018/02/27

Abstract

We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension (m,n). As an application, we study the variety LS^(2,2) of complex Lie superalgebras of dimension (2,2). First we give the algebraic classification and then obtain that LS^(2,2) is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known.

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