Title
A proof of the Tsygan formality conjecture for chains A proof of the Tsygan formality conjecture for chains
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Advances in mathematics. - New York, N.Y.
Volume/pages
179(2003) :1 , p. 7-37
ISSN
0001-8708
ISI
000185640500002
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We extend the Kontsevich formality L∞-morphism to an L∞-morphism of L∞-modules over . The construction of the map is given in Kontsevich-type integrals. The conjecture that such an L∞-morphism exists is due to Boris Tsygan (Formality Conjecture for Chains, math. QA/9904132). As an application, we obtain an explicit formula for isomorphism is the Kontsevich deformation quantization of the algebra A by a Poisson bivector field, and {,} is the Poisson bracket). We also formulate a conjecture extending the Kontsevich theorem on cup-products to this context. The conjecture implies a generalization of the Duflo formula, and many other things.
E-info
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