Connections on smooth Lie algebra bundles
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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.
Key wordsAdjoint bundle Lie algebra bundle Lie connection Lie Ehresmann connection parallel transport universal connection
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The second author is thankful to the SERB/DST, New Delhi, India for the financial assistance SR/S4/MS:856/13. We thank R. Rangarajan for his support.
- 5.H. Gündoğan, Lie algebras of smooth sections, Diploma thesis, Technische Universität Darmstadt, 2007.Google Scholar