Analyticity of a restricted formality

Didier Arnal (1) , Mouna Chaabouni (2) , Mabrouka Hfaiedh (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Laboratoire de Mathématiques de Sfax
3 FSS - Faculté des Sciences de Sfax

The Kontsevich formality can be viewed as a non-linear map ℱ from the L∞ algebra of poly-vector fields on ℝd to the space of poly-differential operators. The space of the half-homogenous poly-vector fields is a sub-L∞ algebra. We prove here that the restriction of ℱ to this subspace is weakly analytic.

Domaines: Mathématiques [math]

Didier Arnal, Mouna Chaabouni, Mabrouka Hfaiedh. Analyticity of a restricted formality. Journal of Mathematical Physics, 2020, 61 (5), pp.053502. ⟨10.1063/1.5142442⟩. ⟨hal-02570916⟩