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Mathematics > Quantum Algebra

arXiv:math/0405177v1 (math)
[Submitted on 10 May 2004 (this version) , latest version 23 May 2004 (v2) ]

Title: Hochschild Cohomology versus De Rham Cohomology without Formality Theorems

Title: 霍奇科恩同调与德雷姆同调无需形式性定理

Authors:Vasiliy Dolgushev (MIT)
Abstract: 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 a symplectic manifold M and the ring H(M, C((h))) of De Rham cohomology of M with the coefficient field C((h)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket induced on H(M,C((h))) via the isomorphism is vanishing. We discuss equivariant properties of the isomorphism and propose an analogue of this statement in an algebraic geometric setting.
Comments: 23 pages, no figures
Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)
Cite as: arXiv:math/0405177 [math.QA]
  (or arXiv:math/0405177v1 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.math/0405177
Journal reference: ITEP-TH-15/04

Submission history

From: Vasiliy Dolgushev [view email]
[v1] Mon, 10 May 2004 23:03:31 UTC (19 KB)
[v2] Sun, 23 May 2004 09:14:24 UTC (20 KB)
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