Decomposition of Lie automorphisms of upper triangular matrix algebra over commutative rings

摘要

Let Tn+1 (R) be the algebra of all upper triangular square matrices of order n + 1 over a commutative ring R with the identity 1 and unit 2. For n >= 2, we prove that any Lie automorphism of Tn+1 (R) can be uniquely written as a product of graph, central, inner and diagonal automorphisms. (c) 2006 Elsevier Inc. All rights reserved.