Algebraic, topological and analytical techniques in differential geometry and geom...
Cohomology of Lie algebroids in the holomorphic and algebraic settings: theory and...
| Full text | |
| Author(s): |
Kotov, Alexei
;
Strobl, Thomas
Total Authors: 2
|
| Document type: | Journal article |
| Source: | LETTERS IN MATHEMATICAL PHYSICS; v. 108, n. 3, p. 20-pg., 2018-03-01. |
| Abstract | |
Cartan-Lie algebroids, i.e., Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids with ad-invariant (Riemannian) metrics on their fibers and base and g, respectively. We determine the necessary and sufficient conditions for a positive quadratic Lie algebroid to integrate to a Riemannian Cartan-Lie groupoid. Here we mean a Cartan-Lie groupoid equipped with a bi-invariant and inversion-invariant metric on such that it induces by submersion the metric g on its base and its restriction to the t-fibers coincides with . (AU) | |
| FAPESP's process: | 11/11973-4 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics |
| Grantee: | Nathan Jacob Berkovits |
| Support Opportunities: | Research Projects - Thematic Grants |