Journal of Noncommutative Geometry

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Volume 14, Issue 1, 2020, pp. 191–222
DOI: 10.4171/JNCG/364

Published online: 2020-05-25

Differential calculus over double Lie algebroids

Sophie Chemla[1]

(1) Sorbonne Université, Paris, France

M. Van den Bergh [20] defined the notion of a double Lie algebroid and showed that a double quasi-Poisson algebra gives rise to a double Lie algebroid.We give new examples of double Lie algebroids and develop a differential calculus in that context. We recover the non commutative Karoubi–de Rham complex [7, 9] and the double Poisson–Lichnerowicz cohomology [16] as particular cases of our construction.

Keywords: Lie–Rinehart algebras, Lie algebroids, double Lie algebroids, double Poisson algebras, Karoubi–de Rham complex

Chemla Sophie: Differential calculus over double Lie algebroids. J. Noncommut. Geom. 14 (2020), 191-222. doi: 10.4171/JNCG/364