Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 891–901 | Cite as

Connections on smooth Lie algebra bundles

  • K. AjaykumarEmail author
  • B. S. KiranagiEmail author


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 words

Adjoint 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.


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Copyright information

© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Department of Studies in MathematicsUniversity of MysoreMysoreIndia

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