Isotopes of~alternative algebras of~characteristic different from~$3$

S. V. Pchelintsev

Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 1002-1015.

Résumé

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.

Détail

Keywords: isotope, identity, Cayley–Dixon algebra, alternative algebra.
Mots-clés : homotope

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