{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:19:17Z","timestamp":1753885157481,"version":"3.41.2"},"reference-count":36,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"FWO","award":["1204019N"],"award-info":[{"award-number":["1204019N"]}]},{"name":"FWO","award":["G083118N"],"award-info":[{"award-number":["G083118N"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Commun. Contemp. Math."],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:p> Adopting the omni-Lie algebroid approach to Dirac\u2013Jacobi structures, we propose and investigate a notion of weak dual pairs in Dirac\u2013Jacobi geometry. Their main motivating examples arise from the theory of multiplicative precontact structures on Lie groupoids. Among other properties of weak dual pairs, we prove two main results. (1) We show that the property of fitting in a weak dual pair defines an equivalence relation for Dirac\u2013Jacobi manifolds. So, in particular, we get the existence of self-dual pairs and this immediately leads to an alternative proof of the normal form theorem around Dirac\u2013Jacobi transversals. (2) We prove the characteristic leaf correspondence theorem for weak dual pairs paralleling and extending analogous results for symplectic and contact dual pairs. Moreover, the same ideas of this proof apply to get a presymplectic leaf correspondence for weak dual pairs in Dirac geometry (not yet present in literature). <\/jats:p>","DOI":"10.1142\/s0219199722500353","type":"journal-article","created":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T07:41:51Z","timestamp":1654760511000},"source":"Crossref","is-referenced-by-count":0,"title":["Weak dual pairs in Dirac\u2013Jacobi geometry"],"prefix":"10.1142","volume":"25","author":[{"given":"Jonas","family":"Schnitzer","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Freiburg, Ernst-Zermelo-Stra\u00dfe 1, D-79104 Freiburg, Germany"}]},{"given":"Alfonso Giuseppe","family":"Tortorella","sequence":"additional","affiliation":[{"name":"Geometry Section, Department of Mathematics, KU Leuven, Celestijnenlaan 200B - 3001 Leuven, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2022,7,16]]},"reference":[{"issue":"22","key":"S0219199722500353BIB001","first-page":"8818","volume":"2020","author":"Blaga A. 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