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

In this article, we find a family SLn,m, in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra Ln,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 SLn,m can be deformed if defined over a field of odd characteristic.