nLab
Lie bialgebroid

Idea

(…something like “Lie algebroid internal to Lie algebroids”, but subtle…)

Definition

Given a Lie algebroid AA together with the structure of a Lie algebroid A *A^* on the dual of the vector bundle underlying AA, the interpretation of a Lie algebroids as a supermanifold as described at Lie infinity-algebroid induces two notions of differentials d Ad_A and d A *d_{A^*} and two notions of Schouten brackets.

A pairs (A,A *)(A,A^*) of Lie algebroids is a Lie bialgebroid if these differentials are derivations of the corresponding Schouten brackets.

See for instance definition 2.2.2 in Roytenberg99.

Remarks

References

  • Roytenberg99 Dmitry Roytenberg, Courant algebroids, derived brackets and even symplectic supermanifolds (arXiv)
Revised on March 1, 2009 03:31:50 by Toby Bartels (71.104.234.95)