Gerstenhaber duality in Hochschild cohomology
(2005) Journal of Pure and Applied Algebra — Vol. 199, n° 1-3, p. 43-59 (2005)
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- Abstract
- Let C be a differential graded chain coalgebra, &UOmega; C the reduced cobar construction on C and C-V the dual algebra. We prove that for a large class of coalgebras C there is a natural isomorphism of Gerstenhaber algebras between the Hochschild cohomologies, HH*(C-V, C-V) and HH*(&UOmega; C; &UOmega; C). This result yields to a Hodge decomposition of the loop space homology of a closed oriented manifold, when the field of coefficients is of characteristic zero. © 2004 Elsevier B.V. All rights reserved.
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Félix, Y., Menichi, L., & Thomas, JC. (2005). Gerstenhaber duality in Hochschild cohomology. Journal of Pure and Applied Algebra, 199(1-3), 43-59. https://doi.org/10.1016/j.jpaa.2004.11.004 (Original work published 2005)