On Poisson superalgebras in characteristic 2

Abstract

This paper is devoted to the study of Poisson superalgebras over fields of characteristic $2$. We investigate their representations, semidirect products, cohomology, formal deformations, and universal enveloping algebras. We also introduce Lie-Rinehart superalgebras in characteristic $2$ and clarify their connections with Poisson superalgebras. In particular, we show that the universal enveloping algebra of a Poisson superalgebra coincides with the universal enveloping algebra of an associated Lie-Rinehart superalgebra. We also compute examples and initiate the study of pre-Poisson superalgebras.