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Nondegenerate invar...
Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
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Krutov, Andrey (author)
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Lebedev, Alexei (author)
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- Leites, Dimitry, 1951- (author)
- Stockholms universitet,Matematiska institutionen,New York University Abu Dhabi, United Arab Emirates
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Shchepochkina, Irina (author)
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(creator_code:org_t)
- Elsevier BV, 2022
- 2022
- English.
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In: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795 .- 1873-1856. ; 649, s. 1-21
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- As is well-known, the dimension of the space spanned by the non-degenerate invariant symmetric bilinear forms (NISes) on any simple finite-dimensional Lie algebra or Lie superalgebra is equal to at most 1 if the characteristic of the algebraically closed ground field is not 2.We prove that in characteristic 2, the superdimension of the space spanned by NISes can be equal to 0, or 1, or 0|1, or 1|1; it is equal to 1|1 if and only if the Lie superalgebra is a queerification (defined in arXiv:1407.1695) of a simple classically restricted Lie algebra with a NIS (for examples, mainly in characteristic ≠2, see arXiv:1806.05505).We give examples of NISes on deformations (with both even and odd parameters) of several simple finite-dimensional Lie superalgebras in characteristic 2.We also recall examples of multiple NISes on simple Lie algebras over non-closed fields.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Restricted Lie algebra
- Simple Lie algebra
- Characteristic 2
- Queerification
Publication and Content Type
- ref (subject category)
- art (subject category)
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