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In this paper we provide a quantization via formality of Poisson actions of a triangular Lie algebra $(mathfrak g,r)$ on a smooth manifold $M$. Using the formality of polydifferential operators on Lie algebroids we obtain a deformation quantization of $M$ together with a quantum group $mathscr{U}_hbar(mathfrak{g})$ and a map of associated DGLAs. This motivates a definition of quantum action in terms of $L_infty$-morphisms which generalizes the one given by Drinfeld.
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the cohomology of th
Let $alpha$ be a quadratic Poisson bivector on a vector space $V$. Then one can also consider $alpha$ as a quadratic Poisson bivector on the vector space $V^*[1]$. Fixed a universal deformation quantization (prediction some weights to all Kontsevich
We introduce a general theory of twisting algebraic structures based on actions of a bialgebra. These twists are closely related to algebraic deformations and also to the theory of quasi-triangular bialgebras. In particular, a deformation produced fr
In this paper we provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This construction allows us to give a constructive proof to Drinfeld theorem and to obtain a concrete formula for Drinfeld twist
The main purpose of this paper is a mathematical construction of a non-perturbative deformation of a two-dimensional conformal field theory. We introduce a notion of a full vertex algebra which formulates a compact two-dimensional conformal field the