Lie algebras of matrices #
An important class of Lie algebras are those arising from the associative algebra structure on square matrices over a commutative ring. This file provides some very basic definitions whose primary value stems from their utility when constructing the classical Lie algebras using matrices.
Main definitions #
lie algebra, matrix
The natural equivalence between linear endomorphisms of finite free modules and square matrices is compatible with the Lie algebra structures.
An invertible matrix induces a Lie algebra equivalence from the space of matrices to itself.
For square matrices, the natural map that reindexes a matrix's rows and columns with equivalent
matrix.reindex, is an equivalence of Lie algebras.