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

Abstract

In this paper, 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.

13 pages, to appear in Communications in Algebra

References in corpus (2)

• Restricted simple Lie (super)algebras in characteristic $3$
• On Solvable Lie and Leibniz Superalgebras with maximal codimension of nilradical