Isotopes of alternative algebras of characteristic different from $3$
- Autores: Pchelintsev S.V.1,2
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Afiliações:
- Financial University under the Government of the Russian Federation
- Moscow Center for Fundamental and Applied Mathematics
- Edição: Volume 84, Nº 5 (2020)
- Páginas: 197-210
- Seção: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/133830
- DOI: https://doi.org/10.4213/im8930
- ID: 133830
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Resumo
We study homotopes of alternative algebras over an algebraically closed field of characteristic different from $3$. We prove an analogue of Albert's theorem on isotopes of associative algebras: in the class of finite-dimensional unital alternative algebras every isotopy is an isomorphism. We also prove that every $(a,b)$-homotope of a unital alternative algebra preserves the identities of the original algebra. We also obtain results on the structure of isotopes of various simple algebras, in particular, Cayley–Dixon algebras.
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Sobre autores
Sergey Pchelintsev
Financial University under the Government of the Russian Federation; Moscow Center for Fundamental and Applied Mathematics
Email: pchelinzev@mail.ru
Doctor of physico-mathematical sciences, Professor
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