Kontsevich star products on the cotangent bundle of a Lie group and integral formulae (Q1600168)

The author constructs natural star products on any cotangent bundle, and characterizes all of them by integral formulae. Using the explicit construction of \textit{S. Gutt} [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)] of a star product on the cotangent bundle \(T^ \ast G\) of a Lie group \(G\) with Lie algebra \(g\), the author shows that any star product on \(g^ \ast\) can be extended to \(T^\ast G\). As a direct consequence, any Kontsevich star product on \(g^\ast\) in the sense of \textit{D. Arnal, N. Ben Amar} and \textit{M. Masmoudi} [Lett. Math. Phys. 48, 291-306 (1999; Zbl 0957.53046)] gives rise to a natural star product on \(T^ \ast G\). In the last part of the paper, he proves how all these extended star products can be written with integral formulae.