Prolongations of Lie Algebra Representations

Hulya Kadioglu; Erdogan Esin; Yusuf Yayli

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arXiv · 1310.2010

Prolongations of Lie Algebra Representations

Hulya Kadioglu·Erdogan Esin·Yusuf Yayli

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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.

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BibTeX RIS

Hulya Kadioglu, Erdogan Esin, Yusuf Yayli. 2013-10-08. Prolongations of Lie Algebra Representations. https://arxiv.org/abs/1310.2010

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