Geodesic
On (α, 1, 0)-Derivations of Anti-Commutative Algebras
Edison Alberto Fernández-Culma1, 2
1Centro de Investigación y Estudios en Matemática, CONICET
2Facultad de Matemática, Universidad Nacional de Córdoba, Argentina
Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 863-872

See the original article notice from the Heldermann Verlag source

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.
Classification: 16W25
Keywords: Anti-commutative algebras, Lie algebras, invariants of algebras, extended derivations of algebras, isomorphism problem

Edison Alberto Fernández-Culma  1 , 2

1 Centro de Investigación y Estudios en Matemática, CONICET
2 Facultad de Matemática, Universidad Nacional de Córdoba, Argentina 
Edison Alberto Fernández-Culma. On (α, 1, 0)-Derivations of Anti-Commutative Algebras. Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 863-872. http://geodesic.mathdoc.fr/item/JOLT_2024_34_4_a5/
@article{JOLT_2024_34_4_a5,
     author = {Edison Alberto Fern\'andez-Culma},
     title = {On (\ensuremath{\alpha}, 1, {0)-Derivations} of {Anti-Commutative} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {863--872},
     year = {2024},
     volume = {34},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_4_a5/}
}
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