Year: 2001
Type: preprint
Abstract: Using a basic idea of Sullivan's rational homotopy theory, one can see a Lie groupoid as the fundamental groupoid of its Lie algebroid. This paper studies analogues of Lie algebroids with non-trivial higher homotopy. Using various homotopy classes one can obtain e.g. central extensions of loop groups, or one can integrate a Lie biagebroid to a double symplectic groupoid. When combined with symplectic geometry, this idea leads to an infinite sequence of notions, starting with sympectic manifolds, Poisson manifolds and Courant algebroids. They are interrelated with higher-dimensional variational problems, and one can use them to define higher-dimensional Hamiltonian mechanics.
Source: arXiv (Cornell University)
Author: Severa, Pavol
Institution: Comenius University Bratislava
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W57692193