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A note on semiprime Malcev superalgebras

Published online by Cambridge University Press:  14 November 2011

Alberto Elduque
Alberto Elduque
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain
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Synopsis

Prime Malcev superalgebras over fields of characteristic not two and three have been studied by Shestakov [8]. He obtains the remarkable result that if these superalgebras have a nonzero odd part then they are Lie superalgebras. The main purpose of this note is to extend this result to fields of characteristic three. To this aim, it is enough to use adequately a result of Filippov [3]. Commutative and anticommutative superalgebras will be considered too, showing that they are prime, semiprime or simple as superalgebras if and only if they are as algebras. Finally, some conclusions for finite-dimensional semisimple Malcev superalgebras will be deduced. Any such superalgebra is the direct sum of a semisimple Lie superalgebra and a direct sum of simple non-Lie algebras.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 5 , 1993 , pp. 887 - 891
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

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