Codimension growth of solvable Lie superalgebras

Abstract

We study numerical invariants of identities of finite-dimensional solvable Lie superalgebras. We define new series of finite-dimensional solvable Lie superalgebras $L$ with non-nilpotent derived subalgebra $L^{\prime }$ and discuss their codimension growth. For the first algebra of this series we prove the existence and integrality of $exp(L)$.