Symbolic Analysis of Lie Algebras
Ian Anderson, Mathematics and Statistics, Utah State University
Abstract: I shall begin this talk by using Maple software to illustrate some standard examples and definitions in the theory of Lie algebras. I shall then survey ongoing efforts to develop software to address a number of outstanding problems in Lie theory, namely: [i] the classification of Lie algebras; [ii] the construction of matrix representations for solvable Lie algebras; [iii] the construction of global Lie groups for solvable Lie algebras; [iv] the classification of Lie subalgebras; [v] the construction of vector field representations of Lie algebras. Applications of this work to the integration of differential equations and to the study of exact solutions to the Einstein equations will be given.