# From Isomorphisms for Lie Algebra-Subalgebra Pairs to Diffeomorphisms for the Equivalence of Space-Times

## Class

Article

## Department

Mathematics and Statistics

## Faculty Mentor

Ian Anderson

## Presentation Type

Oral Presentation

## Abstract

Professor Ian Anderson has developed software for the computer classification of lower dimensional Lie algebras. For computer classification of space-times, the main objects of study in Einstein's theory of general relativity, more is needed. In this presentation I will describe our new software for the classification of Lie algebra-subalgebra pairs. This software is the key tool and an integral part of a larger scheme to determine the equivalence of space-times with symmetry. These equivalences come in the form of diffeomorphisms and can only be computed once an equivalence of particular Lie algebra-subalgebra pairs has been found. This larger scheme will be explained to demonstrate the importance of the new software.

## Start Date

4-9-2015 11:00 AM

From Isomorphisms for Lie Algebra-Subalgebra Pairs to Diffeomorphisms for the Equivalence of Space-Times

Professor Ian Anderson has developed software for the computer classification of lower dimensional Lie algebras. For computer classification of space-times, the main objects of study in Einstein's theory of general relativity, more is needed. In this presentation I will describe our new software for the classification of Lie algebra-subalgebra pairs. This software is the key tool and an integral part of a larger scheme to determine the equivalence of space-times with symmetry. These equivalences come in the form of diffeomorphisms and can only be computed once an equivalence of particular Lie algebra-subalgebra pairs has been found. This larger scheme will be explained to demonstrate the importance of the new software.