Cohomologically rigid solvable Lie superalgebras with model filiform and model nilpotent nilradical

Abstract

In this article, we find a family $S{L}^{n,m},$ in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra $L^{n,m}.$ Moreover, we exhibit a family of cohomologically rigid solvable Lie superalgebras with nilradical the model nilpotent Lie superalgebra of generic characteristic sequence. Both cases correspond to solvable Lie superalgebras of maximal dimension for a given nilradical. Contrariwise, we will show that the family of Lie superalgebras $S{L}^{n,m}$ can be deformed if defined over a field of odd characteristic.

Keywords:

• Cohomology
• Lie superalgebra
• nilpotent Lie superalgebra
• rigid Lie superalgebra
• solvable Lie superalgebra

2020 Mathematics Subject Classification:

• 17B56
• 17B50

Additional information

Funding

The first author was supported by the grant NYUAD-065.