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

Alexander Shchegolev

paper

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

arXiv:1801.05406

Abstract

Every commutator preserving bijection of the unipotent radical $U p (2 n, R)$ of the Borel subgroup of the classical symplectic group of rank at least 4 over a field $F$ such that $6 F = F$ is shown to be the composition of a standard automorphism of $U p (2 n, R)$ and a central map. The latter is a bijection which acts as the right multiplication by a matrix from the center of $U p (2 n, F)$ .