Isotopes of alternative algebras of characteristic different from $3$
- Authors: Pchelintsev S.V.1,2
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Affiliations:
- Financial University under the Government of the Russian Federation
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 84, No 5 (2020)
- Pages: 197-210
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133830
- DOI: https://doi.org/10.4213/im8930
- ID: 133830
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Abstract
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.
Keywords
About the authors
Sergey Valentinovich 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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