{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T05:36:35Z","timestamp":1777613795299,"version":"3.51.4"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,8,11]],"date-time":"2010-08-11T00:00:00Z","timestamp":1281484800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Compositio Math."],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We prove a version of Kontsevich\u2019s formality theorem for two subspaces (branes) of a vector space\n                    <jats:italic>X<\/jats:italic>\n                    . The result implies, in particular, that the Kontsevich deformation quantizations of S(\n                    <jats:italic>X<\/jats:italic>\n                    <jats:sup>*<\/jats:sup>\n                    ) and \u2227(\n                    <jats:italic>X<\/jats:italic>\n                    ) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet\u2019s recent paper on Koszul duality in deformation quantization.\n                  <\/jats:p>","DOI":"10.1112\/s0010437x10004847","type":"journal-article","created":{"date-parts":[[2010,8,11]],"date-time":"2010-08-11T05:38:31Z","timestamp":1281505111000},"page":"105-160","source":"Crossref","is-referenced-by-count":12,"title":["Bimodules and branes in deformation quantization"],"prefix":"10.1017","volume":"147","author":[{"given":"Damien","family":"Calaque","sequence":"first","affiliation":[]},{"given":"Giovanni","family":"Felder","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Ferrario","sequence":"additional","affiliation":[]},{"given":"Carlo A.","family":"Rossi","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,8,11]]},"reference":[{"key":"S0010437X10004847_ref19","first-page":"245","article-title":"Infinity-inner-products on A-infinity-algebras","volume":"3","author":"Tradler","year":"2008","journal-title":"J. Homotopy Relat. Struct."},{"key":"S0010437X10004847_ref16","unstructured":"[16] Shoikhet B. , Koszul duality in deformation quantization and Tamarkin\u2019s approach to Kontsevich formality, Preprint (2008), arXiv:0805.0174, Adv. Math., to appear."},{"key":"S0010437X10004847_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/B:MATH.0000027508.00421.bf"},{"key":"S0010437X10004847_ref10","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1215\/ijm\/1255988267","article-title":"A\u221e-algebras and the cyclic bar complex","volume":"34","author":"Getzler","year":"1990","journal-title":"Illinois J. Math."},{"key":"S0010437X10004847_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2004.10.017"},{"key":"S0010437X10004847_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2006.03.010"},{"key":"S0010437X10004847_ref3","unstructured":"[3] Calaque D. and Rossi C. A. , Lectures on Duflo isomorphisms in Lie algebras and complex geometry, Lecture notes, ETH Z\u00fcrich (2008), available at http:\/\/math.univ-lyon1.fr\/\u223ccalaque\/LectureNotes\/LectETH.pdf."},{"key":"S0010437X10004847_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-007-0179-6"},{"key":"S0010437X10004847_ref4","unstructured":"[4] Calaque D. and Rossi C. A. , Compatibility with cap-products in Tsygan\u2019s formality and homological Duflo isomorphism, Preprint (2008), available at arXiv:0805.2409v2, Lett. Math. Phys., to appear."},{"key":"S0010437X10004847_ref11","doi-asserted-by":"publisher","DOI":"10.4310\/HHA.2001.v3.n1.a1"},{"key":"S0010437X10004847_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00192-0"},{"key":"S0010437X10004847_ref9","doi-asserted-by":"publisher","DOI":"10.1063\/1.2982234"},{"key":"S0010437X10004847_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-004-0609-7"},{"key":"S0010437X10004847_ref17","unstructured":"[17] Tamarkin D. E. , Another proof of M. Kontsevich formality theorem, Preprint (1998), arXiv:math\/9803025v4."},{"key":"S0010437X10004847_ref1","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.2002.203.23"},{"key":"S0010437X10004847_ref12","unstructured":"[12] Keller B. , Derived invariance of higher structures on the Hochschild complex, Preprint (2003), available at http:\/\/people.math.jussieu.fr\/\u223ckeller\/publ\/dih.pdf."},{"key":"S0010437X10004847_ref14","unstructured":"[14] Lef\u00e8vre-Hasegawa K. , Sur les A \u221e -cat\u00e9gories, PhD thesis, Universit\u00e9 Paris 7 (2003), available at http:\/\/people.math.jussieu.fr\/\u223ckeller\/lefevre\/TheseFinale\/tel-00007761.pdf."},{"key":"S0010437X10004847_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01077036"},{"key":"S0010437X10004847_ref15","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1963-0154906-3"},{"key":"S0010437X10004847_ref7","doi-asserted-by":"publisher","DOI":"10.24033\/asens.2082"},{"key":"S0010437X10004847_ref18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010838604927"}],"container-title":["Compositio Mathematica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0010437X10004847","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T08:35:16Z","timestamp":1775205316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0010437X10004847\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,11]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["S0010437X10004847"],"URL":"https:\/\/doi.org\/10.1112\/s0010437x10004847","relation":{},"ISSN":["0010-437X","1570-5846"],"issn-type":[{"value":"0010-437X","type":"print"},{"value":"1570-5846","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,11]]}}}