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

TL;DR

This paper introduces families of cohomologically rigid solvable Lie superalgebras with specific nilradicals, highlighting their maximal dimension and deformation properties over different fields.

Contribution

It constructs new families of cohomologically rigid solvable Lie superalgebras with model filiform and nilpotent nilradicals, and analyzes their deformation behavior.

Findings

Families of cohomologically rigid solvable Lie superalgebras with maximal nilradicals are identified.

Deformations occur for these algebras over fields of odd characteristic.

The constructed families are of maximal dimension for their nilradicals.

Abstract

In this paper, we find a family $SL^{n,m}$, 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 $SL^{n,m}$ can be deformed if defined over a field of odd characteristic.