Title
Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality
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
224(2010) :3 , p. 731-771
ISSN
0001-8708
ISI
000277229200001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
Let α be a quadratic Poisson bivector on a vector space V . Then one can also consider α as a quadratic Poisson bivector on the vector space V∗[1]V∗[1]. Fixed a universal deformation quantization (prediction of some complex weights to all Kontsevich graphs [12]), we have deformation quantization of the both algebras S(V∗)S(V∗) and Λ(V)Λ(V). These are graded quadratic algebras, and therefore Koszul algebras. We prove that for some universal deformation quantization, independent on α, these two algebras are Koszul dual. We characterize some deformation quantizations for which this theorem is true in the framework of the Tamarkin's theory [19].
E-info
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