Codimensions of identities of solvable Lie superalgebras
M. V. Zaicev, D. D. Repov\v{s}
TL;DR
This paper investigates the polynomial identities of solvable Lie superalgebras over characteristic zero fields, demonstrating the existence of finite-dimensional examples with specific codimension growth properties.
Contribution
It constructs examples of solvable Lie superalgebras with non-nilpotent commutator subalgebras where the PI-exponent exists and is an integer.
Findings
Existence of PI-exponent for certain Lie superalgebras
Construction of finite-dimensional solvable Lie superalgebras with specific properties
PI-exponent is an integer in these examples
Abstract
We study identities of Lie superalgebras over a field of characteristic zero. We construct a series of examples of finite-dimensional solvable Lie superalgebras with a non-nilpotent commutator subalgebra for which PI-exponent of codimension growth exists and is an integer number.
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