Derivations of simple three-dimensional anticommutative algebras

  • Sergey V. Pchelintsev Financial University under the Government of the Russian Federation, 49/2 Leningradskij Avenue, Moscow 125167, Russia
  • Maxim S. Dubrovin 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 2nd order.

Author Biographies

Sergey V. Pchelintsev, Financial University under the Government of the Russian Federation, 49/2 Leningradskij Avenue, Moscow 125167, Russia

doctor of science (physics and mathematics); professor at the department of data analysis and machine learning, faculty of information technology and big data analysis



Maxim S. Dubrovin, Moscow City University, 4 Vtoroj Selskohoziajstvenny proezd, 1 building, Moscow 129226, Russia

postgraduate student at the department of mathematical logic, algebra, number theory and discrete mathematics, Institute of Digital Education

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Published
2024-07-17
Keywords: derivation algebras, Lie algebras, simple three-dimensional anticommutative algebras
Supporting Agencies The authors are thankful to the reviewer for the careful reading of the article and for a series of remarks contributing to its improvement.
How to Cite
Pchelintsev, S. V., & Dubrovin, M. S. (2024). Derivations of simple three-dimensional anticommutative algebras. Journal of the Belarusian State University. Mathematics and Informatics, 2, 19-26. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/6029
Issue
No 2 (2024): Journal of the Belarusian State University. Mathematics and Informatics
Section
Mathematical Logic, Algebra and Number Theory

Copyright (c) 2024 Journal of the Belarusian State University. Mathematics and Informatics

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