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
dusan.repovs@guest.arnes.si
Mikhail V. Zaicev
Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russia
zaicevmv@mail.ru
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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