Nonlinear maps preserving Lie products on triangular algebras

Abstract

In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.

Keywords

• Preserver
• Lie product
• Triangular algebra
• Nest algebra