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Deformation of relations Answer to question 2 is the following: a deformation of an algebra $A_0$ parametrized by a pointed affine scheme $*\to X=Spec(B\to k)$ is the data of a $B$-algebra $A$ such t …

The action of GT on deformation quantization has been developed in http://arxiv.org/abs/1009.1654 (Willwacher) and before in http://arxiv.org/abs/math/0202039 (Tamarkin). The fact that GT is Aut(Cha …

Well. Even in the case of a DG (or $A_\infty$) algebra $A$, infinitesimal (i.e. 1st order) deformations are classified by $HH^2(A,A)$. Namely, the structure maps (a-k-a Taylor components) of an $A_\in …

My question is: Does the vanishing of the Poisson bracket plays an important role in finding and proving Duflo's isomorphism theorem? Or it is just an literally first step? Let $A_0$ be a …

Fedosov's work seems to be also available with details in a book Deformation quantization and index theory. Are the two references overlapping ? Yes, indeed. The book contains strictly more than …

This is explained in Section 4.5.2 of "deformation quantization of poisson manifolds" by Kontsevich (http://arxiv.org/abs/q-alg/9709040). The way you wrote the homotopy between two Maurer-Cartan ele …

In addition to the references pointed out by Stefan, I would like to add Déformation, quantification, et théorie de Lie, by Catteno, Keller, and Torossian (Part I and Part III are actually in Engl …

The only way I know to construct a formality quasi-morphism for poy-vector fields out of an homotopy is via Tamarkins approach (i.e. $G_\infty$-formality). What Tamrakin does is prove that there is …

Your question might be Why are infinitesimal deformations typically considered as structures over the ring of dual numbers? A first order (or infinitesimal) deformation of an algebraic stru …

Here is a sketch of topological description of a Tamarkin-Tsygan precalculus. Consider the compactified configuration spaces $C_n$ and $D_{1,n}$ of $n$ points on $\mathbb{R}^2$ and $\mathbb{R}^2-\{( …

The construction is functorial with respect to algebraic morphisms of Lie algebroids (as opposed to geometric ones): see for instance my paper with Van de Bergh https://arxiv.org/pdf/0708.2725.pdf (it …

A $G_\infty$-morphism $\phi$ is determined by structure maps $\phi^{k_1,\dots,k_n}$, $n\geq1$, $k_1,\dots,k_n\geq1$. The $L_\infty$-part of $\phi$ is the $L_\infty$-morphism $\ell$ with structure ma …

Let me try an answer. It seems to me that the appropriate language to use is the one of ringed spaces. For a given ring space $(X,\mathcal{O}_X)$ one can consider the category of sheaves of right $ …

This is probably not really an answer to this question, but there are two different context I know where deformation quantization produces something not exactly associative, but associative in a large …

The answer to your second question is "no", I think. Let's assume that sufficiently nice means that it is a smooth algebraic variety over a field of characteristic $0$. Then, as written in Severin Bar …