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Relevant bibliographies by topics / Kontsevich formality

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Academic literature on the topic 'Kontsevich formality'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Kontsevich formality"

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Calaque, Damien, Giovanni Felder, Andrea Ferrario, and Carlo A. Rossi. "Bimodules and branes in deformation quantization." Compositio Mathematica 147, no. 1 (2010): 105–60. http://dx.doi.org/10.1112/s0010437x10004847.

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AbstractWe prove a version of Kontsevich’s formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X*) and ∧(X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet’s recent paper on Koszul duality in deformation quantization.

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Arnal, Didier. "Kontsevich formality and cohomologies for graphs." Letters in Mathematical Physics 69, no. 1-3 (2004): 205–22. http://dx.doi.org/10.1007/s11005-004-1220-7.

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3

Songhafouo Tsopméné, Paul Arnaud. "Symmetric multiplicative formality of the Kontsevich operad." Journal of Homotopy and Related Structures 13, no. 1 (2017): 225–35. http://dx.doi.org/10.1007/s40062-017-0179-x.

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4

Sharapov, Alexey, and Evgeny Skvortsov. "Formal higher-spin theories and Kontsevich–Shoikhet–Tsygan formality." Nuclear Physics B 921 (August 2017): 538–84. http://dx.doi.org/10.1016/j.nuclphysb.2017.06.005.

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Liao, Hsuan-Yi, Mathieu Stiénon, and Ping Xu. "Formality and Kontsevich–Duflo type theorems for Lie pairs." Advances in Mathematics 352 (August 2019): 406–82. http://dx.doi.org/10.1016/j.aim.2019.04.047.

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6

Shoikhet, Boris. "Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality." Advances in Mathematics 224, no. 3 (2010): 731–71. http://dx.doi.org/10.1016/j.aim.2009.12.010.

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7

Yekutieli, Amnon. "The Continuous Hochschild Cochain Complex of a Scheme." Canadian Journal of Mathematics 54, no. 6 (2002): 1319–37. http://dx.doi.org/10.4153/cjm-2002-051-8.

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AbstractLet X be a separated finite type scheme over a noetherian base ring . There is a complex of topological -modules, called the complete Hochschild chain complex of X. To any -module —not necessarily quasi-coherent—we assign the complex of continuous Hochschild cochains with values in . Our first main result is that when X is smooth over there is a functorial isomorphismin the derived category , where .The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard maps induce a quasi-isomorphismWhen this is the quasi-isomorphism underlyi

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Merkulov, Sergei, and Thomas Willwacher. "Classification of universal formality maps for quantizations of Lie bialgebras." Compositio Mathematica 156, no. 10 (2020): 2111–48. http://dx.doi.org/10.1112/s0010437x20007381.

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We settle several fundamental questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. Moreover, we settle these questions in a greater generality: we give a complete classification of the associated universal formality maps. An important new technical ingredient introduced in this paper is a polydifferential endofunctor ${\mathcal {D}}$ in the category of augmented props with the property that for any representation of a prop ${\mathcal {P}}$ in a vector space $V$ the associated prop ${\mathcal {D}}{

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9

SHOJAEI-FARD, Ali. "Kontsevich Graphons." Kragujevac Journal of Mathematics 47, no. 2 (2023): 213–28. http://dx.doi.org/10.46793/kgjmat2302.213s.

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The article applies graph functions to extend the Kontsevich diﬀerential graded Lie algebraic formalism (in Deformation Quantization) to inﬁnite Kontsevich graphs on the basis of the Connes-Kreimer Hopf algebraic renormalization and the theory of noncommutative diﬀerential geometry.

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Arnal, D., D. Manchon, and M. Masmoudi. "Choix des signes pour la formalité de M. Kontsevich." Pacific Journal of Mathematics 203, no. 1 (2002): 23–66. http://dx.doi.org/10.2140/pjm.2002.203.23.

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Book chapters on the topic "Kontsevich formality"

1

Esposito, Chiara. "Kontsevich’s Formula and Globalization." In Formality Theory. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09290-4_4.

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Conference papers on the topic "Kontsevich formality"

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Jurčo, B. "Noncommutative gauge theories and Kontsevich’s formality theorem." In NEW DEVELOPMENTS IN FUNDAMENTAL INTERACTION THEORIES: 37th Karpacz Winter School of Theoretical Physics. AIP, 2001. http://dx.doi.org/10.1063/1.1419331.

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