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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Aplikace klasifikace C*-algeber: dynamika, geometrie a jejich kvantové analogie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

1873-1856

Svazek periodika

649

Číslo periodika v rámci svazku

September 15

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

000800352000001

EID výsledku v databázi Scopus

2-s2.0-85129458732