Hochschild Cohomology versus De Rham Cohomology without Formality Theorems

Details Hochschild Cohomology versus De Rham Cohomology without Formality Theorems Hochschild Cohomology versus De Rham Cohomology without Formality Theorems

2004-05-10

arxiv.org/abs/math/0405177v2

Int. Math. Res. Not. 2005, no. 21, 1277-1305

Mathematics

Quantum Algebra

23 pages, no figures

Scientific paper

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 the 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.

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