Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring (Q1355596)

The author gives an explicit description of the automorphism group of the Lie algebra \({\mathfrak t}\) of upper triangular \(n\times n\) matrices over a commutative ring with identity. This extends the analogous result of \textit{D. Ž. Doković} [J. Algebra 170, 101-110 (1994; Zbl 0822.17017)] over connected commutative rings. As an application of the result, the author describes the automorphism group of the Lie subalgebra of \({\mathfrak t}\) consisting of all matrices of trace zero in the case when \(n\) is a unit of the ring.