Prolongations of Lie Algebra Representations
Differential Geometry
2016-11-25 v1
Abstract
In this paper, we present a study on the prolongations of representations of Lie algebras. We show that a tangent bundle of a given Lie algebra attains a Lie algebra structure. Then, we prove that this tangent bundle is algebraically isomorphic to the Lie algebra of a tangent bundle of a Lie group. Using these, we define prolongations of representations of Lie algebras. We show that if a Lie algebra representation corresponds to a Lie group representation, then prolongation of Lie algebra representation corresponds to the prolonged Lie group representation.
Cite
@article{arxiv.1310.2010,
title = {Prolongations of Lie Algebra Representations},
author = {Hulya Kadioglu and Erdogan Esin and Yusuf Yayli},
journal= {arXiv preprint arXiv:1310.2010},
year = {2016}
}
Comments
7 pages