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JOURNALS // Journal of the Belarusian State University. Mathematics and Informatics // Archive

Journal of the Belarusian State University. Mathematics and Informatics, 2024 Volume 2, Pages 19–26 (Mi bgumi683)

Mathematical logic, Algebra and Number Theory

Derivations of simple three-dimensional anticommutative algebras

S. V. Pchelintseva, M. S. Dubrovinb

a Financial University under the Government of the Russian Federation, 49/2 Leningradskij Avenue, Moscow 125167, Russia
b Moscow City University, 4 Vtoroj Selskohoziajstvenny proezd, 1 building, Moscow 129226, Russia

Abstract: In this paper, we investigate the derivation algebras of simple three-dimensional anticommutative algebras over algebraically closed fields. The main statement of the article is that the derivation algebras of simple three-dimensional anticommutative algebras have dimensions $0$, $1$ and $3$, for the latter case they are isomorphic to a simple Lie algebra of traceless matrices of the $2^{nd}$ order.

Keywords: derivation algebras; Lie algebras; simple three-dimensional anticommutative algebras

UDC: 512.554

Received: 13.12.2023
Revised: 01.07.2024
Accepted: 01.07.2024

Language: English



© Steklov Math. Inst. of RAS, 2025