Bijective maps on standard Borel subgroup of symplectic group preserving commutators

摘要

Let F be a field, and let $mathbb{G}$ be the standard Borel subgroup of the symplectic group Sp(2m, F). In this paper, we characterize the bijective maps ϕ: $mathbb{G}$ → $mathbb{G}$ satisfying ϕ[x, y] = [ϕ(x), ϕ(y)].