Automorphisms of a linear Lie algebra over a commutative ring
Let \(R\) be a commutative ring with identity. \textit{Y. Cao} showed [J. Algebra 189, No. 2, 506--513 (1997; Zbl 0878.17016)] that each automorphism of \(t\), the Lie algebra of upper triangular matrices over \(R\), is the product of three types of automorphisms: central, graph and inner. In this paper the author shows a similar result for the standard Borel subalgebra of the orthogonal Lie algebra \(o(2m,R)\), where \(m\) is greater than 4 and 2 is invertible in \(R\). It is necessary to find automorphisms to take the place of those in Cao's result.
scientific article; zbMATH DE number 5151570