Cohomology in algebra, geometry, physicsand statistics
Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
Speaker’s name:
Andrey Krutov
Speaker’s affiliation:
Institute of Mathematics of the Czech Academy of Sciences
Place:
in IM building, front building, ground floor, konirna seminar room +ZOOM meeting
Date:
Wednesday, 30. March 2022 - 13:30 to 14:30
Abstract:
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 distinct from 2, see arXiv:1806.05505).
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We shall meet this time at the seminar room KONIRNA, ground floor, front building of IM. We open the seminar room
at 13.15 for coffee and close at 15.00.
Join Zoom Meeting
https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
Meeting ID: 995 9841 3922
Passcode: Galois
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 distinct from 2, see arXiv:1806.05505).
-------------------------------------------------------------------------------------------------------------------------------------
We shall meet this time at the seminar room KONIRNA, ground floor, front building of IM. We open the seminar room
at 13.15 for coffee and close at 15.00.
Join Zoom Meeting
https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
Meeting ID: 995 9841 3922
Passcode: Galois