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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2015 Volume 79, Issue 3, Pages 131–158 (Mi im8251)

This article is cited in 20 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.

UDC: 512.554.5

MSC: 17A70, 17D15, 17D05

Received: 13.05.2014

DOI: 10.4213/im8251


 English version:
Izvestiya: Mathematics, 2015, 79:3, 554–580

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