Solvable and Unipotent Supergroups

A. N. Zubkov; P. A. Ulyashev

doi:10.1007/s10469-014-9284-7

Solvable and Unipotent Supergroups

A. N. Zubkov
, P. A. Ulyashev

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

6 Citations (Scopus)

Abstract

It is proved that an algebraic supergroup G is unipotent iff G_ev is unipotent. Here our reasoning involves only induction on dimension and some properties of the adjoint representation. In a similar way, it is shown that over a field of characteristic zero, a connected supergroup G is solvable iff G_ev is solvable.

Original language	English
Pages (from-to)	206-216
Number of pages	11
Journal	Algebra and Logic
Volume	53
Issue number	3
DOIs	https://doi.org/10.1007/s10469-014-9284-7
Publication status	Published - Jul 2014
Externally published	Yes

Keywords

adjoint representation
algebraic supergroup
connected supergroup
solvable supergroup
unipotent supergroup

ASJC Scopus subject areas

Analysis
Logic

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10.1007/s10469-014-9284-7

Cite this

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title = "Solvable and Unipotent Supergroups",

abstract = "It is proved that an algebraic supergroup G is unipotent iff Gev is unipotent. Here our reasoning involves only induction on dimension and some properties of the adjoint representation. In a similar way, it is shown that over a field of characteristic zero, a connected supergroup G is solvable iff Gev is solvable.",

keywords = "adjoint representation, algebraic supergroup, connected supergroup, solvable supergroup, unipotent supergroup",

author = "Zubkov, \{A. N.\} and Ulyashev, \{P. A.\}",

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AU - Zubkov, A. N.

AU - Ulyashev, P. A.

PY - 2014/7

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N2 - It is proved that an algebraic supergroup G is unipotent iff Gev is unipotent. Here our reasoning involves only induction on dimension and some properties of the adjoint representation. In a similar way, it is shown that over a field of characteristic zero, a connected supergroup G is solvable iff Gev is solvable.

AB - It is proved that an algebraic supergroup G is unipotent iff Gev is unipotent. Here our reasoning involves only induction on dimension and some properties of the adjoint representation. In a similar way, it is shown that over a field of characteristic zero, a connected supergroup G is solvable iff Gev is solvable.

KW - adjoint representation

KW - algebraic supergroup

KW - connected supergroup

KW - solvable supergroup

KW - unipotent supergroup

UR - https://www.scopus.com/pages/publications/84922073632

UR - https://www.scopus.com/pages/publications/84922073632#tab=citedBy

U2 - 10.1007/s10469-014-9284-7

DO - 10.1007/s10469-014-9284-7

M3 - Article

AN - SCOPUS:84922073632

SN - 0002-5232

VL - 53

SP - 206

EP - 216

JO - Algebra and Logic

JF - Algebra and Logic

IS - 3

ER -

Solvable and Unipotent Supergroups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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