Hochschild Cohomology versus De Rham Cohomology without Formality Theorems
Quantum Algebra
2007-05-23 v2 High Energy Physics - Theory
Differential Geometry
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 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.
Keywords
Cite
@article{arxiv.math/0405177,
title = {Hochschild Cohomology versus De Rham Cohomology without Formality Theorems},
author = {Vasiliy Dolgushev},
journal= {arXiv preprint arXiv:math/0405177},
year = {2007}
}
Comments
23 pages, no figures