Formality theorem with coefficients in a module

Simple item page
dc.creatorChemla, Sophie
dc.date2006-04-18
dc.date2008-01-15
dc.date.accessioned2026-07-07T08:54:24Z
dc.date.available2026-07-07T08:54:24Z
dc.descriptionIn this article, $X$ will denote a ${\cal C}^{\infty}$ manifold. In a very famous article, Kontsevich showed that the differential graded Lie algebra (DGLA) of polydifferential operators on $X$ is formal. Calaque extended this theorem to any Lie algebroid. More precisely, given any Lie algebroid $E$ over $X$, he defined the DGLA of $E$-polydifferential operators, $Γ(X, ^{E}D^{*}_{poly})$, and showed that it is formal. Denote by $Γ(X, ^{E}T^{*}_{poly})$ the DGLA of $E$-polyvector fields. Considering $M$, a module over $E$, we define $Γ(X, ^{E}T_{poly}^{*}(M))$ the $Γ(X, ^{E}T^{*}_{poly})$-module of $E$-polyvector fields with values in $M$. Similarly, we define the $Γ(X, ^{E}D^{*}_{poly})$-module of $E$-polydifferential operators with values in $M$, $Γ(X, ^{E}D^{*}_{poly}(M))$. We show that there is a quasi-isomorphism of $L_{\infty}$-modules over $Γ(X, ^{E}T^{*}_{poly})$ from $Γ(X, ^{E}T^{*}_{poly}(M))$ to $Γ(X, ^{E}D^{*}_{poly}(M))$. Our result extends Calaque 's (and Kontsevich's) result.
dc.description44 pages. I removed the second formality theorem and improved the part about applications
dc.identifierhttps://arxiv.org/abs/math/0604386
dc.identifierhttp://arxiv.org/abs/math/0604386
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145922
dc.subjectQuantum Algebra
dc.subject17B66 (Primary), 16E45 (Secondary)
dc.titleFormality theorem with coefficients in a module
dc.typetext

Files

Collections

arXiv