Connections on smooth Lie algebra bundles

Ajaykumar, K. and Kiranagi, B. S. (2019) Connections on smooth Lie algebra bundles. Indian Journal of Pure and Applied Mathematics, 50 (4). ISSN 0019-5588

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Abstract

We define the notion of Lie Ehresmann connection on Lie algebra bundles and show that a Lie connection on a Lie algebra bundle induces a Lie Ehresmann connection. The converse is proved for normed Lie algebra bundles. We then show that the connection on adjoint bundle corresponding to the connection on principal G—bundle to which it is associated is a Lie Ehresmann connection. Further it is shown that the Lie Ehresmann connection on adjoint bundle induced by a universal G-connection is universal over the family of adjoint bundles associated to G-bundles. © 2019, Indian National Science Academy.

Item Type:	Article
Uncontrolled Keywords:	Adjoint bundle; Lie algebra bundle; Lie connection; Lie Ehresmann connection; parallel transport; universal connection
Subjects:	E Mathematical Science > Mathematics
Divisions:	Department of > Mathematics
Depositing User:	C Swapna Library Assistant
Date Deposited:	20 Nov 2025 07:28
Last Modified:	20 Nov 2025 07:28
URI:	http://eprints.uni-mysore.ac.in/id/eprint/17944

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