On split Lie superalgebras

We study the structure of arbitrary split Lie superalgebras. We show that any of such superalgebras L is of the form L = U + ∑ j I j with U a subspace of the Abelian (graded) subalgebra H and any I j , a well described (graded) ideal of L satisfying [ I j , I k ] = 0 if j ≠ k . Under certain conditi...

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Bibliographic Details
Published in:Journal of mathematical physics 2010-07, Vol.51 (7), p.073511-073511-9
Main Authors: CALDERON MARTIN, Antonio J, SANCHEZ DELGADO, José M
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
Vector space
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Summary:We study the structure of arbitrary split Lie superalgebras. We show that any of such superalgebras L is of the form L = U + ∑ j I j with U a subspace of the Abelian (graded) subalgebra H and any I j , a well described (graded) ideal of L satisfying [ I j , I k ] = 0 if j ≠ k . Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal (graded) ideals, each one being a simple split Lie superalgebra.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3464265