๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Automorphisms of Certain Lie Algebras of Upper Triangular Matrices over a Commutative Ring

โœ Scribed by You'an Cao

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
187 KB
Volume
189
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices over R and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the automorphism group of the Lie algebra t, which extends a result given by Dokovic. In addition, we explicitly describe the automorphism group of the Lie algebra b when n is a unit of R.

๐Ÿ“œ SIMILAR VOLUMES

Automorphisms of the Lie Algebra of Uppe
Automorphisms of the Lie Algebra of Upper Triangular Matrices over a Connected Commutative Ring
โœ D.Z. Dokovic ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 276 KB

Let \(R\) be a non-trivial commutative ring having no idempotents except 0 and 1 . Denote by \(t\) the Lie algebra over \(R\) consisting of all upper triangular \(n\) by \(n\) matrices over \(R\). We give an explicit description of the automorphism group of this Lie algebra. 1994 Academic Press, Inc