Journal of Lie Theory 34 (2024), No. 4, 863--872
Copyright Heldermann Verlag 2024
On (α, 1, 0)-Derivations of Anti-Commutative Algebras
Edison Alberto Fernández-Culma
Centro de Investigación y Estudios en Matemática, CONICET
and: Facultad de Matemática, Universidad Nacional de Córdoba, Argentina
efernandez@famaf.unc.edu.ar
The aim of this paper is to investigate (α, 1, 0)-derivations of anti-commutative algebras. We show that when the base field is of characteristic zero, the dimensions of the spaces of (α, 1, 0)-derivations yield an infinite one-parameter family of invariant functions under algebra isomorphism. Furthermore, we demonstrate that this infinite family reduces to only three distinct functions when we restrict our focus to the class of Lie algebras. This reduction addresses an open problem regarding the behavior of these invariants in the context of Lie algebras. Additionally, we establish sharp bounds for these invariant functions.
Keywords: Anti-commutative algebras, Lie algebras, invariants of algebras, extended derivations of algebras, isomorphism problem.
MSC: 16W25.
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