Abstract: Action Lie groupoids are used to model spaces of orbits of actions of Lie groups on manifolds. For each such action groupoid $M\rtimes H$ we construct a locally convex bialgebroid $\mathord{\mathrm{Dirac}}(M\rtimes H)$ with an antipode over $\mathord{\mathcal{C}^{\infty}_{c}}(M)$, from which the groupoid $M\rtimes H$ can be reconstructed as its spectral action Lie groupoid $\mathord{\mathcal{AG}_{\mathit{sp}}}(\mathord{\mathrm{Dirac}}(M\rtimes H))$.Keywords: action Lie groupoid, coalgebra, Dirac distribution, Hopf algebroid, transversal distributionPublished in DiRROS: 16.02.2024; Views: 171; Downloads: 51 Full text (491,64 KB)This document has many files! More...
