On the Duflo formula for $L_\infty$-algebras and Q-manifolds

arXivmath/9812009MaRDI QIDQ6501109

Boris Shoikhet

Abstract: We prove a direct analogue of the classical Duflo formula in the case of $L_{i}nfty$-algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When $G$ is a compact connected Lie group, the Duflo theorem for the Q-manifold $(PiTG,d_{DR})$ is exactly the Duflo theorem for the Lie algebra $g=LieG$. The corresponding theorem for the Q-manifold $(PiTM,d_{DR})$, where $M$ is an arbitrary smooth manifold, is a generalization of the Duflo theorem for the case of smooth manifolds. On the other hand, the Duflo theorem for the Q-manifold $$, where $M$ is a complex manifold, is a generalization of the M. Kontsevich's ``theorem on complex manifold [K1], Sect. 8.4.

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