Polyvector fields and polydifferential operators associated with Lie pairs
Ruggero Bandiera
Sapienza Università di Roma, ItalyMathieu Stiénon
Pennsylvania State University, University Park, USAPing Xu
Pennsylvania State University, University Park, USA
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Abstract
We prove that the spaces and associated with a Lie pair each carry an algebra structure canonical up to an isomorphism with the identity map as linear part. These two spaces serve, respectively, as replacements for the spaces of formal polyvector fields and formal polydifferential operators on the Lie pair . Consequently, both and admit unique Gerstenhaber algebra structures. Our approach is based on homotopy transfer and the construction of a Fedosov dg Lie algebroid (i.e. a dg foliation on a Fedosov dg manifold).
Cite this article
Ruggero Bandiera, Mathieu Stiénon, Ping Xu, Polyvector fields and polydifferential operators associated with Lie pairs. J. Noncommut. Geom. 15 (2021), no. 2, pp. 643–711
DOI 10.4171/JNCG/416