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

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.