Centers of centralizers of nilpotent elements in exceptional Lie superalgebras

Leyu Han

doi:10.1142/S0219498822500530

Centers of centralizers of nilpotent elements in exceptional Lie superalgebras

Leyu Han

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let 𝖌=𝖌_0̅⊕𝖌_1̅ be a finite-dimensional simple Lie superalgebra of type D(2,1;α), G(3) or F(4) over C. Let G be the simply connected semisimple algebraic group over ℂ such that Lie(G)=𝖌_0̅. Suppose e∈𝖌_0̅ is nilpotent. We describe the centralizer 𝖌^e of e in 𝖌 and its centre 𝖟(𝖌^e) especially. We also determine the labelled Dynkin diagram for e. We prove theorems relating the dimension of (𝖟(𝖌^e))^Ge and the labelled Dynkin diagram.

Original language	English
Article number	2250053
Number of pages	31
Journal	Journal of Algebra and Its Applications
Volume	21
Issue number	03
DOIs	https://doi.org/10.1142/S0219498822500530
Publication status	Published - 7 Jan 2021

Keywords

nilpotent elements
labelled Dynkin diagrams
Lie superalgebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0219498822500530

Cite this

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title = "Centers of centralizers of nilpotent elements in exceptional Lie superalgebras",

abstract = "Let 햌=햌0̅⊕햌1̅ be a finite-dimensional simple Lie superalgebra of type D(2,1;α), G(3) or F(4) over C. Let G be the simply connected semisimple algebraic group over ℂ such that Lie(G)=햌0̅. Suppose e∈햌0̅ is nilpotent. We describe the centralizer 햌e of e in 햌 and its centre 햟(햌e) especially. We also determine the labelled Dynkin diagram for e. We prove theorems relating the dimension of (햟(햌e))Ge and the labelled Dynkin diagram.",

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T1 - Centers of centralizers of nilpotent elements in exceptional Lie superalgebras

AU - Han, Leyu

PY - 2021/1/7

Y1 - 2021/1/7

N2 - Let 햌=햌0̅⊕햌1̅ be a finite-dimensional simple Lie superalgebra of type D(2,1;α), G(3) or F(4) over C. Let G be the simply connected semisimple algebraic group over ℂ such that Lie(G)=햌0̅. Suppose e∈햌0̅ is nilpotent. We describe the centralizer 햌e of e in 햌 and its centre 햟(햌e) especially. We also determine the labelled Dynkin diagram for e. We prove theorems relating the dimension of (햟(햌e))Ge and the labelled Dynkin diagram.

AB - Let 햌=햌0̅⊕햌1̅ be a finite-dimensional simple Lie superalgebra of type D(2,1;α), G(3) or F(4) over C. Let G be the simply connected semisimple algebraic group over ℂ such that Lie(G)=햌0̅. Suppose e∈햌0̅ is nilpotent. We describe the centralizer 햌e of e in 햌 and its centre 햟(햌e) especially. We also determine the labelled Dynkin diagram for e. We prove theorems relating the dimension of (햟(햌e))Ge and the labelled Dynkin diagram.

KW - nilpotent elements

KW - labelled Dynkin diagrams

KW - Lie superalgebras

UR - https://arxiv.org/abs/2203.04423

U2 - 10.1142/S0219498822500530

DO - 10.1142/S0219498822500530

M3 - Article

VL - 21

JO - Journal of Algebra and Its Applications

JF - Journal of Algebra and Its Applications

IS - 03

M1 - 2250053

ER -

Centers of centralizers of nilpotent elements in exceptional Lie superalgebras

Abstract

Keywords

ASJC Scopus subject areas

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