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Izvestiya: Mathematics, 2015, Volume 79, Issue 3, Pages 554–580
DOI: https://doi.org/10.1070/IM2015v079n03ABEH002753 (Mi im8251) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero

S. V. Pchelintseva, O. V. Shashkovb

a Financial University under the Government of the Russian Federation, Moscow
b Moscow State Regional Institute of Humanities
English version PDF (397 kB) Citations (21)
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DOI: https://doi.org/10.1070/IM2015v079n03ABEH002753
Abstract: We classify simple finite-dimensional right-alternative superalgebras $A=A_0\oplus A_1$ over a field of characteristic zero in which the even part $A_0$ is associative and commutative, while $A_1$ is an associative $A_0$-bimodule. We prove that every such superalgebra $A=A_0\oplus A_1$ is obtained by doubling the semisimple even part $A_0$, and the multiplication in $A$ is defined using a suitable automorphism and a linear operator acting on $A_0$.
Keywords: simple superalgebra, right-alternative superalgebra.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00014
This research was supported by the Russian Foundation for Basic Research (grant no. 14-01-00014).
Received: 13.05.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 3, Pages 131–158
DOI: https://doi.org/10.4213/im8251
Bibliographic databases:
Document Type: Article
UDC: 512.554.5
MSC: 17A70, 17D15, 17D05
Language: English
Original paper language: Russian
Citation: S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero”, Izv. RAN. Ser. Mat., 79:3 (2015), 131–158; Izv. Math., 79:3 (2015), 554–580
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:145
    English version PDF:10
    References:62
    First page:32
     
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