Pullback of lie algebra and lie group bundles, and their homotopy invariance

Document Type : Research Paper

Authors

1 School of PPSH, Chinmaya Vishwavidyapeeth, Adi Sankara Nilayam, Ernakulam, Kerala, India

2 Department of Mathematics, University of Mysore,Mysuru

3 Department of Mathematics, University of Mysore, Mysuru

Abstract

We study the pullback Lie algebra (group) bundle of a Lie algebra (group) bundle and show that the Lie algebra bundle of the pullback of a Lie group bundle $\mathfrak{G}$ is isomorphic to the pullback of the Lie algebra bundle of $\mathfrak{G}$. Then, using the notion of Lie connection on a Lie algebra bundle, we show that the pullbacks of a Lie algebra bundle $\xi$ over a smooth manifold $M$ with respect to two smooth homotopic functions $f_0 , f_1 : N \rightarrow M$ are isomorphic to Lie algebra bundles over $N$.

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Journal of Algebra and Related Topics
Volume 8, Issue 1
June 2020
Pages 15-26

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