Papers by Shahlo Ergasheva
Ural mathematical journal, Dec 29, 2022
In the present paper, we study simple algebras, which do not belong to the well-known classes of ... more 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 finitedimensional algebras over a field of characteristic 0 without finite basis of identities, constructed by Kislitsin, are such algebras. In the present paper, we consider two such algebras: the simple seven-dimensional anticommutative algebra D and the seven-dimensional central simple commutative algebra C. We prove that every local derivation of these algebras D and C is a derivation, and every 2-local derivation of these algebras D and C is also a derivation. We also prove that every local automorphism of these algebras D and C is an automorphism, and every 2-local automorphism of these algebras D and C is also an automorphism.
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Papers by Shahlo Ergasheva