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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
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.
Received: 13.05.2014
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
Linking options:
https://www.mathnet.ru/eng/im8251https://doi.org/10.1070/IM2015v079n03ABEH002753 https://www.mathnet.ru/eng/im/v79/i3/p131
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Abstract page: | 635 | Russian version PDF: | 145 | English version PDF: | 10 | References: | 62 | First page: | 32 |
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