Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will introduce the concept of a higher algebroid - the notion generalizing Lie algebroids and higher order tangent bundles. Our approach (joint works with Michał Jóźwikowski) is based on the description of a (Lie) algebroid as a vector bundle comorphism (Zakrzewski morphism) - a relation of special kind. In case of the Lie algebroid of a Lie groupoid G such a relation is obtained by a (natural) reduction of the canonical involution T T G -> T T G and it has a direct generalization when T G is replaced with the higher order tangent bundle of G. The discussed notion of a k-th order (Lie) algebroid (k\geq 1) has a rich algebraic structure and is very natural from the perspective of a geometric formalism of a k-th order variational calculus.
I will also discuss the other concept of higher order analogs of Lie algebroids present in the literature.
Meeting ID: 840 5801 4241 Passcode: algebroid