Orbifold cup products and ring structures on Hochschild cohomologies

@article{Pflaum2007OrbifoldCP,
  title={Orbifold cup products and ring structures on Hochschild cohomologies},
  author={Markus J. Pflaum and Hessel B. Posthuma and X. Tang and Hsian-hua Tseng},
  journal={arXiv: K-Theory and Homology},
  year={2007}
}
In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In… Expand
Braided Hochschild cohomology and Hopf actions
  • C. Negron
  • Mathematics
  • Journal of Noncommutative Geometry
  • 2019
We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give aExpand
The Hochschild cohomology ring of a global quotient orbifold
We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-equivariant sheaf ofExpand
Dunkl operator and quantization of ℤ2-singularity
Abstract Let (X, ω) be a symplectic orbifold which is locally like the quotient of a ℤ2 action on ℝn. Let be a deformation quantization of X constructed via the standard Fedosov method withExpand
Noncommutative Poisson structures on orbifolds
Author(s): Halbout, Gilles; Tang, Xiang | Abstract: In this paper, we compute the Gerstenhaber bracket on the Hoch-schild cohomology of $C^\infty(M)\rtimes G$ for a finite group $G$ acting on aExpand
Finite groups acting linearly: Hochschild cohomology and the cup product
Abstract When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebraExpand
Cyclic cocycles on deformation quantizations and higher index theorems
Abstract We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex ofExpand
The periodic cyclic homology of crossed products of finite type algebras
We study the periodic cyclic homology groups of the cross-product of a finite type algebra $A$ by a discrete group $\Gamma$. In case $A$ is commutative and $\Gamma$ is finite, our results areExpand
Orbifolds and their quantizations as noncommutative geometries
Orbifolds are a natural generalization of the concept of a manifold with a rich geometric structure. In particular, its orbifold cohomology has many surprising features, most notably a ring structureExpand
Non-commutative Poisson Structure on Non-commutative Algebraic Torus Orbifolds
We study the Gerstenhaber algebra structure on the algebraic non-commutative torus(also called quantum torus) orbifolds resulting by the action of finite subgroups of $SL_2(\mathbb Z)$. We alsoExpand
Cyclic homology and group actions
Abstract In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete)Expand
...
1
2
...

References

SHOWING 1-10 OF 56 REFERENCES
Hochschild cohomology of quantized symplectic orbifolds and the Chen-Ruan cohomology
We prove the additive version of the conjecture proposed by Ginzburg and Kaledin. This conjecture states that if X/G is an orbifold modeled on a quotient of a smooth affine symplectic variety X (overExpand
A deRham model for Chen-Ruan cohomology ring of Abelian orbifolds
We present a deRham model for Chen-Ruan cohomology ring of abelian orbifolds. We introduce the notion of twist factors so that formally the stringy cohomology ring can be defined without goingExpand
Noncommutative Poisson structures on orbifolds
Author(s): Halbout, Gilles; Tang, Xiang | Abstract: In this paper, we compute the Gerstenhaber bracket on the Hoch-schild cohomology of $C^\infty(M)\rtimes G$ for a finite group $G$ acting on aExpand
Hochschild Cohomology versus De Rham Cohomology without Formality Theorems
We exploit the Fedosov-Weinstein-Xu (FWX) resolution proposed in q-alg/9709043 to establish an isomorphism between the ring of Hochschild cohomology of the quantum algebra of functions on aExpand
An algebraic index theorem for orbifolds
Abstract Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem forExpand
Homology of formal deformations of proper étale Lie groupoids
Abstract In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper étale Lie groupoid is studied. We compute the HochschildExpand
Multiplicative structure on the Hochschild cohomology of crossed product algebras
Consider a smooth affine algebraic variety $X$ over an algebraically closed field, and let a finite group $G$ act on it. We assume that the characteristic of the field is greater than the dimensionExpand
Poisson deformations of symplectic quotient singularities
Abstract We establish a connection between smooth symplectic resolutions and symplectic deformations of a (possibly singular) affine Poisson variety. In particular, let V be a finite-dimensionalExpand
Cyclic Cohomology of Etale Groupoids; The General Case
We give a general method for computing the cyclic cohomology of crossed products by etale groupoids, extending the Feigin-Tsygan-Nistor spectral sequences. In particular we extend the computationsExpand
On Two Theorems about Symplectic Reflection Algebras
We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of theExpand
...
1
2
3
4
5
...