Explicit homotopy formula for Hochschild (co)homology

Authors
Citation
G. Halbout, Explicit homotopy formula for Hochschild (co)homology, CR AC S I, 329(9), 1999, pp. 757-762
Citations number
6
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
329
Issue
9
Year of publication
1999
Pages
757 - 762
Database
ISI
SICI code
0764-4442(19991101)329:9<757:EHFFH(>2.0.ZU;2-N
Abstract
Let k be the field C or R, let M be the space k(n) nod let A be the algebra of polynomials over M. We produce a general explicit homotopy formula betw een the complex of Hochschild chains of A, (C.(A), b) and the de Rhan compl ex of M, (Omega. (M), 0). This formula can be generalized when M is a contr actible open set in a complex manifold and A is the space of holomorphic fu nctions over M. Then we find a new, homotopy formula for rite Hochschild co homology of the algebra of smooth fonctions over M different from the one g iven in [5]. Finally, we show how this formula carl be used to construct a homotopy for the cyclic homology. (C) 1999 Academie des Sciences/Editions s cientifiques et medicales Elsevier SAS.