Geodesic
On (α, 1, 0)-Derivations of Anti-Commutative Algebras
Journal of Lie theory, Tome 34 (2024) no. 4, pp. 863-872
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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
Mots-clés : Anti-commutative algebras, Lie algebras, invariants of algebras, extended derivations of algebras, isomorphism problem 
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     author = {E. A. Fern\~A{\textexclamdown}ndez-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/JLT_2024_34_4_JLT_2024_34_4_a5/}
}
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E. A. Fernández-Culma. On (α, 1, 0)-Derivations of Anti-Commutative Algebras. Journal of Lie theory, Tome 34 (2024) no. 4, pp. 863-872. http://geodesic.mathdoc.fr/item/JLT_2024_34_4_JLT_2024_34_4_a5/