Geodesic
Derivations of simple three-dimensional anticommutative algebras
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2024), pp. 19-26.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{BGUMI_2024_2_a1,
     author = {S. V. Pchelintsev and M. S. Dubrovin},
     title = {Derivations of simple three-dimensional anticommutative algebras},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {19--26},
     publisher = {mathdoc},
     volume = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a1/}
}
TY  - JOUR
AU  - S. V. Pchelintsev
AU  - M. S. Dubrovin
TI  - Derivations of simple three-dimensional anticommutative algebras
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2024
SP  - 19
EP  - 26
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a1/
LA  - ru
ID  - BGUMI_2024_2_a1
ER  - 
%0 Journal Article
%A S. V. Pchelintsev
%A M. S. Dubrovin
%T Derivations of simple three-dimensional anticommutative algebras
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2024
%P 19-26
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a1/
%G ru
%F BGUMI_2024_2_a1
S. V. Pchelintsev; M. S. Dubrovin. Derivations of simple three-dimensional anticommutative algebras. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2024), pp. 19-26. http://geodesic.mathdoc.fr/item/BGUMI_2024_2_a1/

[1] I. B. Kaygorodov, YuS. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izvestiya. Mathematics, 78(5) (2014), 922–936 | DOI

[2] V. V. Gorbatsievich, “Anticommutative finite-dimensional algebras of the first three levels of complexity”, Algebra i analiz, 5(3) (1993), 100–118

[3] A. P. Elisova, “Local derivations and local automorphisms of nilpotent algebras of matrices of small orders”, Siberian Aerospace Journal, 13(4) (2012), 17–22

[4] ShA. Ayupov, F. N. Arzikulov, “2-Local derivations on algebras of matrix-valued functions on a compactum”, Vladikavkazskii matematicheskii zhurnal, 20(1) (2018), 38–49 | DOI

[5] N. Jacobson, Lie algebras, Interscience, New York, 1962, +331 pp.

[6] N. Jacobson, Structure and representations of Jordan algebras, American Mathematical Society, Providence, 1968, +461 pp.

[7] R. D. Schafer, An introduction to nonassociative algebras, Academic Press, New York, 1966, +177 pp.

[8] I. N. Herstein, Noncommutative rings, Mathematical Association of America, 1968, +199 pp.

[9] F. Arzikulov, O. Samsaqov, “Description of local multipliers on finite-dimensional associative algebras”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2023), 32–41

[10] A. A. Krylov, S. V. Pchelintsev, “The isotopically simple algebras with a nil-basis”, Communications in Algebra, 48(4) (2020), 1697–1712 | DOI