Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring
Title:
Derivations of the intermediate Lie algebras between the Lie algebra of diagonal matrices and that of upper triangular matrices over a commutative ring
Author:
Wang, Dengyin Ou, Shikun Yu, Qiu
Appeared in:
Linear & multilinear algebra
Paging:
Volume 54 (2005) nr. 5 pages 369-377
Year:
2005-09-01
Contents:
Let R be an arbitrary commutative ring with identity, gl(n, R) the general linear Lie algebra over R consisting of all n × n matrices over R and with the bracket operation [x, y] = xy - yx, t (resp., u) the Lie subalgebra of gl(n, R) consisting of all n × n upper triangular (resp., strictly upper triangular) matrices over R and d the Lie subalgebra of gl(n, R) consisting of all n × n diagonal matrices over R. The aim of this article is to give an explicit description of the derivation algebras of the intermediate Lie algebras between d and t.