相关论文: A cohomological construction of modules over Fedos…
In this paper, we study deformation quantization of symplectic vector fields \`a la Fedosov. We show that each symplectic vector field can be quantized to a derivation of the deformed star algebra. Moreover, we show that this quantization…
In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [VdB]. More precisely, we consider the class of algebras $A$ such that there exists an invertible bimodule…
We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…
On a symplectic manifold $M$, the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let $\hbar$ denote the parameter. Associated to them is the quantum $\mathcal{D}$ -…
In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
Let (M, \om) be a symplectic manifold. A Lagrangian fiber bundle \pi : M -> B determines a completely integrable system on M. First integrals of this system are the pull-backs of functions on the base of the bundle. We show that for each…
Given a $C_\infty$ coalgebra $C_*$, a strict dg Hopf algebra $H_*$, and a twisting cochain $\tau:C_* \rightarrow H_*$ such that $Im(\tau) \subset Prim(H_*)$, we describe a procedure for obtaining an $A_\infty$ coalgebra on $C_* \otimes…
For a star product with separation of variables * on a pseudo-Kaehler manifold we give a simple closed formula of the total symbol of the left star multiplication operator L_f by a given function f. The formula for the star product f * g…
Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one…
We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal…
We construct new examples of left bialgebroids and Hopf algebroids, arising from noncommutative geometry. Given a first order differential calculus $\Omega$ on an algebra $A$, with the space of left vector fields $\mathfrak{X}$, we…
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of…
It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg-Witten map can be…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…
If H is a finite dimensional Hopf algebra, C. Cibils and M. Rosso found an algebra X having the property that Hopf bimodules over H^* coincide with left X-modules. We find two other algebras, Y and Z, having the same property; namely, Y is…
A differential geometric version of noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. For start, a noncommutative manifold is considered as a product space X = Y * Z,…
Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of…
This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the…
We obtain a family of strict $\hat G$-invariant products on the space of holomorphic functions on a semisimple coadjoint orbit of a complex connected semisimple Lie group $\hat G$. By restriction, we also obtain strict $G$-invariant…