Abstract
We show that the second Hochschild cohomology space for the space of smooth functions on a manifold corresponding to cochains defined by continuous operators is the same as the one corresponding to differentiable operators, i.e. is given by the space of skewsymmetric contravariant 2-tensors on the manifold. We do this using a coboundary construction due to Omori, Maeda and Yoshioka.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bertelson, M., Cahen, M. and Gutt, S.: Equivalence of star products, Classical Quantum Gravity (to appear).
Cahen, M., De Wilde, M. and Gutt, S.: Local cohomology of the algebra of smooth functions on a connected manifold, Lett. Math. Phys. 4 (1980), 157–167.
Gutt, S.: Déformations formelles de l’algèbre des fonctions différentielles sur une variété symplectique, Thèse, Université Libre de Bruxelles, 1980.
Omori, H., Maeda, Y, and Yoshioka, A.: Deformation quantizations of Poisson algebras, in: Contemp. Math. 179, Amer. Math. Soc., Providence, 1994, pp. 213–240.
Vey, J.: Déformation du crochet de Poisson sur une variété symplectique, Comment. Math. Helv. 50 (1975) 421–454.
Pinczon, G.: On the equivalence between continuous and differential deformation theories, Lett. Math. Phys. 39 (1997), 143–156.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gutt, S. On Some Second Hochschild Cohomology Spaces for Algebras of Functions on a Manifold. Letters in Mathematical Physics 39, 157–162 (1997). https://doi.org/10.1023/A:1007330711440
Issue Date:
DOI: https://doi.org/10.1023/A:1007330711440