Abstract:
We study simple finite-dimensional right-alternative unital
superalgebras over a field of characteristic zero.
We prove that if the even part of a superalgebra is
associative and commutative, then the superalgebra is
of Abelian type. The classification of such superalgebras is known.
Keywords:
simple superalgebra, right-alternative superalgebra, superalgebra of Abelian type.
Citation:
S. V. Pchelintsev, O. V. Shashkov, “Simple finite-dimensional right-alternative unital superalgebras
with associative-commutative even part over a field of characteristic zero”, Izv. Math., 82:3 (2018), 578–595
\Bibitem{PchSha18}
\by S.~V.~Pchelintsev, O.~V.~Shashkov
\paper Simple finite-dimensional right-alternative unital superalgebras
with associative-commutative even part over a~field of characteristic zero
\jour Izv. Math.
\yr 2018
\vol 82
\issue 3
\pages 578--595
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Linking options:
https://www.mathnet.ru/eng/im8651
https://doi.org/10.1070/IM8651
https://www.mathnet.ru/eng/im/v82/i3/p136
This publication is cited in the following 9 articles:
S. V. Pchelintsev, O. V. Shashkov, “Simple right alternative superalgebras”, J. Math. Sci., 284:4 (2024), 527–544
O. V. Shashkov, “Right alternative superalgebras of capacity 1 with strongly alternative even part”, Algebra and Logic, 59:2 (2020), 180–195
S. V. Pchelintsev, O. V. Shashkov, “Simple right-alternative superalgebras with semisimple even part”, Siberian Math. J., 61:2 (2020), 304–321
O. V. Shashkov, “Finite-dimensional unital right alternative superalgebras with strongly alternative even part”, Siberian Math. J., 61:5 (2020), 926–940
O. V. Shashkov, “Ob osnovnoi teoreme Vedderberna dlya pravoalternativnykh superalgebr emkosti 1”, Sib. elektron. matem. izv., 17 (2020), 1571–1579
S. V. Pchelintsev, O. V. Shashkov, “Linearly generated singular superalgebras”, J. Algebra, 546 (2020), 580–603
S. V. Pchelintsev, O. V. Shashkov, “Simple right-alternative unital superalgebras over an algebra of matrices of order 2”, Algebra and Logic, 58:1 (2019), 77–94
L. S. I. Murakami, S. V. Pchelintsev, O. V. Shashkov, “Finite-dimensional right alternative superalgebras with semisimple strongly alternative even part”, J. Algebra, 528 (2019), 150–176
S. V. Pchelintsev, O. V. Shashkov, “Singulyarnye 6-mernye superalgebry”, Sib. elektron. matem. izv., 15 (2018), 92–105
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