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arXiv · 2109.13093

Convolution bialgebra of a Lie groupoid and transversal distributions

J. Kalisnik·J. Mrcun
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Abstract

For a Lie groupoid G over a smooth manifold M we construct the adjoint action of the etale Lie groupoid G# of germs of local bisections of G on the Lie algebroid g of G. With this action, we form the associated convolution C_c(M)/R-bialgebra C_c(G#,g). We represent this C_c(M)/R-bialgebra in the algebra of transversal distributions on G. This construction extends the Cartier-Gabriel decomposition of the Hopf algebra of distributions with finite support on a Lie group.

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BibTeXRIS

J. Kalisnik, J. Mrcun. 2021-09-27. Convolution bialgebra of a Lie groupoid and transversal distributions. https://doi.org/10.1016/j.geomphys.2022.104642

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