Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00556911" target="_blank" >RIV/67985840:_____/22:00556911 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.laa.2022.04.020" target="_blank" >https://doi.org/10.1016/j.laa.2022.04.020</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2022.04.020" target="_blank" >10.1016/j.laa.2022.04.020</a>
Alternative languages
Result language
angličtina
Original language name
Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
1873-1856
Volume of the periodical
649
Issue of the periodical within the volume
September 15
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
1-21
UT code for WoS article
000800352000001
EID of the result in the Scopus database
2-s2.0-85129458732