Geodesic
Isotopes of~alternative algebras of~characteristic different from~$3$
Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 1002-1015

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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: isotope, identity, Cayley–Dixon algebra, alternative algebra.
Mots-clés : homotope 
@article{IM2_2020_84_5_a7,
     author = {S. V. Pchelintsev},
     title = {Isotopes of~alternative algebras of~characteristic different from~$3$},
     journal = {Izvestiya. Mathematics },
     pages = {1002--1015},
     publisher = {mathdoc},
     volume = {84},
     number = {5},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a7/}
}
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S. V. Pchelintsev. Isotopes of~alternative algebras of~characteristic different from~$3$. Izvestiya. Mathematics , Tome 84 (2020) no. 5, pp. 1002-1015. http://geodesic.mathdoc.fr/item/IM2_2020_84_5_a7/