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Izvestiya: Mathematics, 2020, Volume 84, Issue 5, Pages 1002–1015
DOI: https://doi.org/10.1070/IM8930 (Mi im8930) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Isotopes of alternative algebras of characteristic different from $3$

S. V. Pchelintsevab

a Financial University under the Government of the Russian Federation, Moscow
b Moscow Center for Fundamental and Applied Mathematics
English version PDF (480 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM8930
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: homotope, isotope, identity, Cayley–Dixon algebra, alternative algebra.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics
This research was supported by a grant from the Moscow Centre for Fundamental and Applied Mathematics of Moscow State University: “Structure theory and combinatorially logical methods in the theory of algebraic systems”.
Received: 07.05.2019
Revised: 03.09.2019
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2020, Volume 84, Issue 5, Pages 197–210
DOI: https://doi.org/10.4213/im8930
Bibliographic databases:
Document Type: Article
UDC: 512.554
MSC: 17D05
Language: English
Original paper language: Russian
Citation: S. V. Pchelintsev, “Isotopes of alternative algebras of characteristic different from $3$”, Izv. RAN. Ser. Mat., 84:5 (2020), 197–210; Izv. Math., 84:5 (2020), 1002–1015
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8930
  • https://www.mathnet.ru/eng/im/v84/i5/p197
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:26
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