On lie superalgebras of aAlgebraic supergroups

Bin Shu; Lisun Zheng

doi:10.1142/s1005386709000352

On lie superalgebras of aAlgebraic supergroups

Bin Shu^*
, Lisun Zheng

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

5 Scopus citations

Abstract

Let G be an algebraic supergroup over a field k, whose pure-even group scheme G_ev is a reduced algebraic group scheme, i.e., k[G _ev = k[G]/(k[G]k[G]_1̄ is reduced. In this paper, we prove that Lie(G) can be identified with the Lie superalgebra of admissible left-invariant derivations of k[G].

Original language	English
Pages (from-to)	361-370
Number of pages	10
Journal	Algebra Colloquium
Volume	16
Issue number	3
DOIs	https://doi.org/10.1142/s1005386709000352
State	Published - Sep 2009

Keywords

Admissible derivation
Algebraic supergroup
Distribution algebra

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10.1142/s1005386709000352

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title = "On lie superalgebras of aAlgebraic supergroups",

abstract = "Let G be an algebraic supergroup over a field k, whose pure-even group scheme Gev is a reduced algebraic group scheme, i.e., k[G ev = k[G]/(k[G]k[G]{\=1} is reduced. In this paper, we prove that Lie(G) can be identified with the Lie superalgebra of admissible left-invariant derivations of k[G].",

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author = "Bin Shu and Lisun Zheng",

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doi = "10.1142/s1005386709000352",

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AU - Shu, Bin

AU - Zheng, Lisun

PY - 2009/9

Y1 - 2009/9

N2 - Let G be an algebraic supergroup over a field k, whose pure-even group scheme Gev is a reduced algebraic group scheme, i.e., k[G ev = k[G]/(k[G]k[G]1̄ is reduced. In this paper, we prove that Lie(G) can be identified with the Lie superalgebra of admissible left-invariant derivations of k[G].

AB - Let G be an algebraic supergroup over a field k, whose pure-even group scheme Gev is a reduced algebraic group scheme, i.e., k[G ev = k[G]/(k[G]k[G]1̄ is reduced. In this paper, we prove that Lie(G) can be identified with the Lie superalgebra of admissible left-invariant derivations of k[G].

KW - Admissible derivation

KW - Algebraic supergroup

KW - Distribution algebra

UR - https://www.scopus.com/pages/publications/68149179465

U2 - 10.1142/s1005386709000352

DO - 10.1142/s1005386709000352

M3 - 文章

AN - SCOPUS:68149179465

SN - 1005-3867

VL - 16

SP - 361

EP - 370

JO - Algebra Colloquium

JF - Algebra Colloquium

IS - 3

ER -

On lie superalgebras of aAlgebraic supergroups

Abstract

Keywords

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