Bijective PC-maps of the unipotent radical of the Borel subgroup of the classical symplectic group

Research output

Abstract

We classify the commutator preserving bijections of the unipotent radical Up(2n, F) of the Borel subgroup of the classical symplectic group of rank at least 2 over a field F such that 6F=F. Every such a bijection is shown to be the composition of a standard automorphism of Up(2n, F) and a central map. The latter is the identity modulo the centre of (2n, F).

Original languageEnglish
Number of pages36
JournalLinear and Multilinear Algebra
Early online date1 Jun 2019
DOIs
Publication statusPublished - 12 Jun 2019

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Symplectic Group
Classical Groups
Bijective
Bijection
Subgroup
Commutator
Automorphism
Modulo
Classify
Standards

Scopus subject areas

  • Algebra and Number Theory

Cite this

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abstract = "We classify the commutator preserving bijections of the unipotent radical Up(2n, F) of the Borel subgroup of the classical symplectic group of rank at least 2 over a field F such that 6F=F. Every such a bijection is shown to be the composition of a standard automorphism of Up(2n, F) and a central map. The latter is the identity modulo the centre of (2n, F).",
keywords = "automorphisms, Lie product preservers, PC-maps, Symplectic group, unipotent group, unitriangular matrices, LIE-ALGEBRAS, AUTOMORPHISMS, LINEAR-MAPS",
author = "Alexander Shchegolev",
year = "2019",
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doi = "10.1080/03081087.2019.1627276",
language = "English",
journal = "Linear and Multilinear Algebra",
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AB - We classify the commutator preserving bijections of the unipotent radical Up(2n, F) of the Borel subgroup of the classical symplectic group of rank at least 2 over a field F such that 6F=F. Every such a bijection is shown to be the composition of a standard automorphism of Up(2n, F) and a central map. The latter is the identity modulo the centre of (2n, F).

KW - automorphisms

KW - Lie product preservers

KW - PC-maps

KW - Symplectic group

KW - unipotent group

KW - unitriangular matrices

KW - LIE-ALGEBRAS

KW - AUTOMORPHISMS

KW - LINEAR-MAPS

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