{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:45:16Z","timestamp":1757313916700,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,1,9]],"date-time":"2011-01-09T00:00:00Z","timestamp":1294531200000},"content-version":"vor","delay-in-days":373,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Netherlands Organisation for Scientific Research","doi-asserted-by":"crossref","award":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"],"award-info":[{"award-number":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"crossref"}]},{"name":"SNF","award":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"],"award-info":[{"award-number":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"]}]},{"name":"SNF","award":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"],"award-info":[{"award-number":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"]}]},{"name":"SNF","award":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"],"award-info":[{"award-number":["613.000.602","200020-107444\/1","21-65213.01","PA002-113136"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Given a symplectic manifold <jats:italic>M<\/jats:italic>, we may define an operad structure\non the the spaces <jats:italic>O<\/jats:italic><jats:sup><jats:italic>k<\/jats:italic><\/jats:sup> of the Lagrangian submanifolds of  via\nsymplectic reduction. If <jats:italic>M<\/jats:italic> is also a symplectic groupoid, then its multiplication\nspace is an associative product in this operad. Following this idea, we provide\na deformation theory for symplectic groupoids analog to the deformation\ntheory of algebras. It turns out that the semiclassical part of Kontsevich\u2032s\ndeformation of <jats:italic>C<\/jats:italic><jats:sup><jats:italic>\u221e<\/jats:italic><\/jats:sup>(<jats:italic>\u211d<\/jats:italic><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>) is a deformation of the trivial symplectic groupoid\nstructure of <jats:italic>T<\/jats:italic><jats:sup>\u2217<\/jats:sup><jats:italic>\u211d<\/jats:italic><jats:sup><jats:italic>d<\/jats:italic><\/jats:sup>.<\/jats:p>","DOI":"10.1155\/2010\/643605","type":"journal-article","created":{"date-parts":[[2011,1,9]],"date-time":"2011-01-09T19:38:19Z","timestamp":1294601899000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Formal Lagrangian Operad"],"prefix":"10.1155","volume":"2010","author":[{"given":"Alberto S.","family":"Cattaneo","sequence":"first","affiliation":[]},{"given":"Benoit","family":"Dherin","sequence":"additional","affiliation":[]},{"given":"Giovanni","family":"Felder","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,1,9]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:MATH.0000027508.00421.bf"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00220\u2010004\u20101199\u2010z"},{"key":"e_1_2_6_3_2","unstructured":"CattaneoA. S. The Lagrangian operad http:\/\/www.math.unizh.ch\/reports\/05_05.pdf."},{"key":"e_1_2_6_4_2","unstructured":"DherinB. Star products and symplectic groupoids Ph.D. thesis 2004 ETH Z\u00fcrich."},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05018-7"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1515\/form.2004.002"},{"key":"e_1_2_6_7_2","series-title":"Mathematical Surveys and Monographs","volume-title":"Operads in Algebra, Topology and Physics","author":"Markl M.","year":"2002"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.4310\/JSG.2010.v8.n2.a4"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/S1073792895000110"},{"key":"e_1_2_6_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11005\u2010005\u20100034\u20106"},{"key":"e_1_2_6_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00316669"},{"key":"e_1_2_6_12_2","series-title":"Nouvelle S\u00e9rie A","volume-title":"Groupo\u00efdes Symplectiques","author":"Coste A.","year":"1987"},{"key":"e_1_2_6_13_2","first-page":"235","article-title":"The Maslov quantization conditions in higher cohomology and analogs of notions developed in Lie theory for canonical fibre bundles of symplectic manifolds II","volume":"8","author":"Karas\u00ebv M. V.","year":"1989","journal-title":"Selecta Mathematica Sovietica"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02097706"},{"key":"e_1_2_6_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00220\u2010005\u20101336\u20103"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2010\/643605.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2010\/643605.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2010\/643605","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T16:31:39Z","timestamp":1718728299000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2010\/643605"}},"subtitle":[],"editor":[{"given":"A.","family":"Zayed","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1155\/2010\/643605"],"URL":"https:\/\/doi.org\/10.1155\/2010\/643605","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2010,1]]},"assertion":[{"value":"2010-07-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-12-07","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-01-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"643605"}}