Hochschild Cohomology versus De Rham Cohomology without Formality Theorems
نویسنده
چکیده
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((~))) of De Rham cohomology of M with the coefficient field C((~)) without making use of any version of formality theorem. We also show that the Gerstenhaber bracket induced on H(M,C((~))) via the isomorphism is vanishing. We discuss equivariant properties of the isomorphism and propose an analogue of this statement in an algebraic geometric setting.
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