Convolution bialgebra of a Lie groupoid and transversal distributions
Quantum Algebra
2022-10-25 v1 Differential Geometry
Operator Algebras
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.
Cite
@article{arxiv.2109.13093,
title = {Convolution bialgebra of a Lie groupoid and transversal distributions},
author = {J. Kalisnik and J. Mrcun},
journal= {arXiv preprint arXiv:2109.13093},
year = {2022}
}
Comments
22 pages