We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the category of integrable Lie algebroids and complete Lie algebroid comorphisms to the category of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplec…
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This work explores higher-order algebroids via vector bundle comorphisms.
problem Generalizing concepts of higher-order tangent bundles and Lie algebroids.
method Introduces a vector bundle comorphism approach to describe higher-order algebroids.
result Establishes a one-to-one correspondence between higher-order Lie algebroids and specific algebraic structures.
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach higher algebroids are vector bundle comorphism between g…
Study sheaves of Lie-Rinehart algebras and their morphisms, generalizing Lie algebroid concepts.
problem Understanding sheaves of Lie-Rinehart algebras and their morphisms.
method Introduced morphisms and comorphisms, proved factorization theorems, and defined higher homotopy groups and groupoids.
result Sheaves of Lie-Rinehart algebras over smooth manifolds induce partitions into orbits of the fundamental groupoid.