A CHARACTERIZATION OF DERIVATIONS ON ISAYEV-KISLITSIN ALGEBRAS
A CHARACTERIZATION OF DERIVATIONS ON ISAYEV-KISLITSIN ALGEBRAS
DOI:
https://doi.org/10.52754/16948645_2023_2_33Keywords:
Simple algebra, Derivation, Local derivation, 2-Local derivation, Automorphism, Local automorphism, 2-Local automorphism, Basis of identitiesAbstract
In the present paper we study simple algebras, which do not belong to the well-known classes of algebras (associative algebras, alternative algebras, Lie algebras, Jordan algebras, etc.). The simple finite-dimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Isayev and Kislitsin, are such algebras. In the present paper we consider such algebras: the simple seven-dimensional algebra . We prove that every local derivation of the algebra is a derivation, and every 2-local derivation of the algebra is also a derivation. We also prove that every local automorphism of the algebra is an automorphism, and every 2-local automorphism of the algebra is also an automorphism.
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