Symbolic Analysis of Lie Algebras

Ian Anderson, Mathematics and Statistics, Utah State University

Wednesday November 16th, 2005 at 3:30pm in K9509.


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.