In mathematics, a Lie algebroid is a vector bundle A → M {\displaystyle A\rightarrow M} together with a Lie bracket on its space of sections Γ ( A ) {\displaystyle...

or Lie algebras. Algebroid branch, a formal power series branch of an algebraic curve Algebroid cohomology Algebroid multifunction Courant algebroid, an...

manifold M {\displaystyle M} , where G {\displaystyle G} is a Lie group, is the Lie algebroid of the gauge groupoid of P {\displaystyle P} . Explicitly,...

a Lie bialgebroid consists of two compatible Lie algebroids defined on dual vector bundles. Lie bialgebroids are the vector bundle version of Lie bialgebras...

usually not employed in symplectic geometry, such as the theory of Lie groupoids and algebroids. Moreover, there are natural examples of structures which should...

the correspondence between Lie groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by...

field [X, Y]. This turns the vector fields with the Lie bracket into a Lie algebroid. Vanishing of the Lie bracket of X and Y means that following the flows...

In mathematics, R-algebroids are constructed starting from groupoids. These are more abstract concepts than the Lie algebroids that play a similar role...

Principal homogeneous space Invariant theory Lie derivative Darboux derivative Lie groupoid Lie algebroid Lattice (group) Lattice (discrete subgroup) Frieze...

standard example and the double of a Lie bialgebra are special instances of Courant algebroids. A Courant algebroid consists of the data a vector bundle...