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Journal of Lie Theory 28 (2018), No. 4, 1189--1199
Copyright Heldermann Verlag 2018

Codimension Growth of Solvable Lie Superalgebras

Dusan D. Repovs
Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, 1000, Slovenia

Mikhail V. Zaicev
Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russia

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 $L'$ and discuss their codimension growth. For the first algebra of this series we prove the existence and integrality of exp(L).

Keywords: Polynomial identities, Lie superalgebras, graded identities, codimensions, exponential growth.

MSC: 17B01, 16P90; 15A30, 16R10

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