### 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 language | English |
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Number of pages | 36 |

Journal | Linear and Multilinear Algebra |

Early online date | 1 Jun 2019 |

DOIs | |

Publication status | Published - 12 Jun 2019 |

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### Scopus subject areas

- Algebra and Number Theory

### Cite this

}

TY - JOUR

T1 - Bijective PC-maps of the unipotent radical of the Borel subgroup of the classical symplectic group

AU - Shchegolev, Alexander

PY - 2019/6/12

Y1 - 2019/6/12

N2 - 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).

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

UR - http://www.scopus.com/inward/record.url?scp=85067517853&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/bijective-pcmaps-unipotent-radical-borel-subgroup-classical-symplectic-group

U2 - 10.1080/03081087.2019.1627276

DO - 10.1080/03081087.2019.1627276

M3 - Article

AN - SCOPUS:85067517853

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

ER -