{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:49:38Z","timestamp":1772297378219,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Eur. Math. Soc."],"published-print":{"date-parts":[[2012,3,7]]},"abstract":"<jats:p>\n                    We prove the universal lifting theorem: for an\n                    <jats:inline-formula>\n                      <jats:tex-math>\\alpha<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -simply connected and\n                    <jats:inline-formula>\n                      <jats:tex-math>\\alpha<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -connected Lie groupoid\n                    <jats:inline-formula>\n                      <jats:tex-math>\\Gamma<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    with Lie algebroid\n                    <jats:inline-formula>\n                      <jats:tex-math>A<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , the graded Lie algebra of multi-differentials on\n                    <jats:inline-formula>\n                      <jats:tex-math>A<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is isomorphic to that of multiplicative multi-vector fields on\n                    <jats:inline-formula>\n                      <jats:tex-math>\\Gamma<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases.The second goal of the paper is the study of basic properties of quasi-Poisson groupoids. In particular, we prove that a group pair\n                    <jats:inline-formula>\n                      <jats:tex-math>(D, G)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    associated to a Manin quasi-triple\n                    <jats:inline-formula>\n                      <jats:tex-math>(\\mathfrak d, \\mathfrak g, \\mathfrak h)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    induces a quasi-Poisson groupoid on the transformation groupoid\n                    <jats:inline-formula>\n                      <jats:tex-math>G\\times D\/G\\rightrightarrows D\/G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . Its momentum map corresponds exactly with the\n                    <jats:inline-formula>\n                      <jats:tex-math>D\/G<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -momentum map of Alekseev and Kosmann-Schwarzbach.\n                  <\/jats:p>","DOI":"10.4171\/jems\/315","type":"journal-article","created":{"date-parts":[[2012,3,7]],"date-time":"2012-03-07T17:45:35Z","timestamp":1331142335000},"page":"681-731","source":"Crossref","is-referenced-by-count":26,"title":["Universal lifting theorem and quasi-Poisson groupoids"],"prefix":"10.4171","volume":"14","author":[{"given":"David","family":"Iglesias-Ponte","sequence":"first","affiliation":[{"name":"(CSIC-UAM-UCM-UC3M), Madrid, Spain"}]},{"given":"Camille","family":"Laurent-Gengoux","sequence":"additional","affiliation":[{"name":"Universidade de Coimbra, Portugal"}]},{"given":"Ping","family":"Xu","sequence":"additional","affiliation":[{"name":"University of Luxembourg, Luxembourg"}]}],"member":"2673","container-title":["Journal of the European Mathematical Society"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/JEMS\/315","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:59:10Z","timestamp":1762869550000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/jems\/315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,7]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/jems\/315","relation":{},"ISSN":["1435-9855","1435-9863"],"issn-type":[{"value":"1435-9855","type":"print"},{"value":"1435-9863","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,7]]}}}