Isotopes of alternative algebras of characteristic different from $3$
- Autores: Pchelintsev S.1,2
-
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://journals.rcsi.science/1607-0046/article/view/133830
- DOI: https://doi.org/10.4213/im8930
- ID: 133830
Citar
Acesso aberto
Acesso está concedido
Somente assinantes
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.
Palavras-chave
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
Bibliografia
- A. A. Albert, “Non-associative algebras. I. Fundamental concepts and isotopy”, Ann. of Math. (2), 43:4 (1942), 685–707
- R. D. Schafer, “Alternative algebras over an arbitrary field”, Bull. Amer. Math. Soc., 49:8 (1943), 549–555
- K. McCrimmon, “Homotopes of alternative algebras”, Math. Ann., 191:4 (1971), 253–262
- M. Babikov, “Isotopy and identities in alternative algebras”, Proc. Amer. Math. Soc., 125:6 (1997), 1571–1575
- С. В. Пчелинцев, “Изотопы первичных $(-1,1)$- и йордановых алгебр”, Алгебра и логика, 49:3 (2010), 388–423
- V. I. Glizburg, S. V. Pchelintsev, “Isotopes of simple algebras of arbitrary dimension”, Asian-Eur. J. Math., 2020, 2050108, 19 pp.
- N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., 39, Amer. Math. Soc., Providence, RI, 1968, x+453 pp.
- К. А. Жевлаков, А. М. Слинько, И. П. Шестаков, А. И. Ширшов, Кольца, близкие к ассоциативным, Наука, М., 1978, 431 с.
- С. В. Пчелинцев, “Первичные альтернативные алгебры, близкие к коммутативным”, Изв. РАН. Сер. матем., 68:1 (2004), 183–206
- С. В. Пчелинцев, “Вырожденные альтернативные алгебры”, Сиб. матем. журн., 55:2 (2014), 396–411
- С. В. Пчелинцев, “Изотопы альтернативного монстра и алгебры Скосырского”, Сиб. матем. журн., 57:4 (2016), 850–865
- A. A. Krylov, S. V. Pchelintsev, “The isotopically simple algebras with a nil-basis”, Comm. Algebra, 48:4 (2020), 1697–1712
- R. H. Bruck, “Some results in the theory of linear non-associative algebras”, Trans. Amer. Math. Soc., 56 (1944), 141–199
- M. Zorn, “Theorie der alternativen Ringe”, Abh. Math. Sem. Univ. Hamburg, 8:1 (1931), 123–147
- R. D. Schafer, “The Wedderburn principal theorem for alternative algebras”, Bull. Amer. Math. Soc., 55:6 (1949), 604–614
- R. D. Schafer, An introduction to nonassociative algebras, Pure Appl. Math., 22, New York–London, Academic Press, 1966, x+166 pp.
- A. A. Albert, “The structure of right alternative algebras”, Ann. of Math. (2), 59:3 (1954), 408–417
- И. М. Михеев, “О простых правоальтернативных кольцах”, Алгебра и логика, 16:6 (1977), 682–710
- В. Г. Скосырский, “Правоальтернативные алгебры”, Алгебра и логика, 23:2 (1984), 185–192
- С. В. Пчелинцев, “Коммутаторные тождества гомотопов $(-1,1)$-алгебр”, Сиб. матем. журн., 54:2 (2013), 417–435
