Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero
Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 554-580
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{IM2_2015_79_3_a4,
author = {S. V. Pchelintsev and O. V. Shashkov},
title = {Simple finite-dimensional right-alternative superalgebras of {Abelian} type of characteristic zero},
journal = {Izvestiya. Mathematics },
pages = {554--580},
publisher = {mathdoc},
volume = {79},
number = {3},
year = {2015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a4/}
}
TY - JOUR AU - S. V. Pchelintsev AU - O. V. Shashkov TI - Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero JO - Izvestiya. Mathematics PY - 2015 SP - 554 EP - 580 VL - 79 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a4/ LA - en ID - IM2_2015_79_3_a4 ER -
%0 Journal Article %A S. V. Pchelintsev %A O. V. Shashkov %T Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero %J Izvestiya. Mathematics %D 2015 %P 554-580 %V 79 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a4/ %G en %F IM2_2015_79_3_a4
S. V. Pchelintsev; O. V. Shashkov. Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero. Izvestiya. Mathematics , Tome 79 (2015) no. 3, pp. 554-580. http://geodesic.mathdoc.fr/item/IM2_2015_79_3_a4/