Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2

0556911 - MÚ 2023 RIV US eng J - Článek v odborném periodiku
Krutov, Andrey - Lebedev, A. - Leites, D. - Shchepochkina, I.
Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2.
Linear Algebra and Its Applications. Roč. 649, September 15 (2022), s. 1-21. ISSN 0024-3795. E-ISSN 1873-1856
Grant CEP: GA ČR(CZ) GJ20-17488Y
Institucionální podpora: RVO:67985840
Klíčová slova: Lie superalgebra * non-degenerate invariant symmetric bilinear form * queerification * restricted Lie algebra
Obor OECD: Pure mathematics
Impakt faktor: 1.1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.laa.2022.04.020

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.
Trvalý link: http://hdl.handle.net/11104/0331621