Differential calculus over double Lie algebroids
Sophie Chemla
TL;DR
This paper introduces new examples of double Lie algebroids and develops a differential calculus framework that generalizes non-commutative de Rham complexes and double Poisson-Lichnerowicz cohomology.
Contribution
It provides novel examples of double Lie algebroids and a unified differential calculus encompassing existing non-commutative geometric structures.
Findings
Recovered non-commutative de Rham complex as a special case.
Derived double Poisson-Lichnerowicz cohomology within the new framework.
Extended the theory of double Lie algebroids with explicit examples.
Abstract
The notion of double Lie algebroid was defined by M. Van den Bergh and was illustrated by the double quasi Poisson case. We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative de Rham complex and the double Poisson-Lichnerowicz cohomology (Pichereau-vanWeyer) as particular cases of our construction.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.