On cohomologies and algebraic $K$-theory of Lie $p$-superalgebras

Abstract

An enveloping associative superalgebra $\Lambda [L,\alpha ,\beta ]$ and its groups of cohomologies are defined and it is proved that there exists Frobenius multiplication of the Quillen algebraic $K$-functors of $\Lambda [L,\alpha ,\beta ]$. These results generalize corresponding results for Lie $p$-algebras which were proved by the author earlier.