Connections on smooth Lie algebra bundles

K. Ajaykumar () and B. S. Kiranagi ()
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K. Ajaykumar: University of Mysore
B. S. Kiranagi: University of Mysore

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 4, 891-901

Abstract: 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.

Keywords: Adjoint bundle; Lie algebra bundle; Lie connection; Lie Ehresmann connection; parallel transport; universal connection (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0362-3

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