We propose a generalization of the momentum map on symplectic manifold with Lie algebra action to Courant algebroid structure. The theory section is generalized compatible algebroid. As an example, we identify in constrained Hamiltonian mechanics symmetry. Moreover, construct cohomological formulations by considering BFV and BV formalism this system. Weil for structure constructed.

In categorified symplectic geometry, one studies the categorified algebraic and geometric structures that naturally arise on manifolds equipped with a closed non-degenerate n + 1-form. The case relevant to classical string theory is when n = 2 and is called ‘2-plectic geometry’. Just as the Poisson bracket makes the smooth functions on a symplectic manifold into a Lie algebra, there is a Lie 2-...

<p style='text-indent:20px;'>The core diagram of a double Lie algebroid consists the algebroid, together with two core-anchor maps to sides algebroid. If these core-anchors are surjective, then and its called <i>transitive</i>. This paper establishes an equivalence between transitive algebroids, diagrams over fixed base manifold. In other words, it proves that is completely de...

In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off–diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries and local anisotropy and define certain generalizations of manifolds with Killing and/ or Lie algebra symmetries. For Lie algebroids, there are structures func...

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of com...

In this paper we revisit the family of algebroid space curves defined by Moh and find an explicit minimal generating set for defining ideal.