{"id":624,"date":"2025-09-14T07:17:53","date_gmt":"2025-09-14T05:17:53","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/gentle\/?p=624"},"modified":"2025-09-14T07:23:49","modified_gmt":"2025-09-14T05:23:49","slug":"obstructions-to-the-existence-of-a-dirac-complement","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/gentle\/2025\/09\/14\/obstructions-to-the-existence-of-a-dirac-complement\/","title":{"rendered":"Obstructions to the existence of a Dirac complement"},"content":{"rendered":"<p>16 Sep 2025. Poster by Tom Ariel at the meeting of the Spanish Network of Geometry and Physics, Barcelona.<\/p>\n<p>Abstract: Dirac structures are a geometric object generalizing symplectic and Poisson structures. From a physics viewpoint, they describe mechanical systems with both symmetries and constraints. Geometrically, they are given by subbundles of a vector bundle with additional structure, called a Courant algebroid. A pair of complementary Dirac structures in a Courant algebroid decomposes it as the double of a Lie bialgebroid. Our goal is to describe, in a given Courant algebroid, the obstruction to the existence of a Dirac complement for a given Dirac structure. Our main result provides an algebraic obstruction in terms of curved differential graded Lie algebras to the existence of a Dirac complement.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>16 Sep 2025. Poster by Tom Ariel at the meeting of the Spanish Network of Geometry and Physics, Barcelona. Abstract: Dirac structures are a geometric object generalizing symplectic and Poisson structures. From a physics viewpoint, they describe mechanical systems with both symmetries and constraints. Geometrically, they are given by subbundles of a vector bundle with [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30,26],"tags":[],"class_list":["post-624","post","type-post","status-publish","format-standard","hentry","category-ariel","category-talks"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/624","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/comments?post=624"}],"version-history":[{"count":2,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/624\/revisions"}],"predecessor-version":[{"id":628,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/posts\/624\/revisions\/628"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/media?parent=624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/categories?post=624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/gentle\/wp-json\/wp\/v2\/tags?post=624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}