Algebroids associated to the groupoid of partially invertible elements of a -algebra
arXiv:1401.0810 · doi:10.1016/j.geomphys.2015.05.003
Abstract
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a -algebra. In particular the complex analytic manifold structure of these objects is investigated. The expressions on the Lie brackets for A and related algebroids are given in noncommutative operator coordinates in the explicit way. We also prove statements describing structure of the groupoid of partial isometries and the frame groupoid of A as well as the structure of their algebroids.
34 pages