{"id":5131,"date":"2016-07-02T05:37:22","date_gmt":"2016-07-02T05:37:22","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=5131"},"modified":"2016-07-02T05:37:22","modified_gmt":"2016-07-02T05:37:22","slug":"kirillov-structures-up-to-homotopy","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2016\/07\/02\/kirillov-structures-up-to-homotopy\/","title":{"rendered":"Kirillov structures up to homotopy"},"content":{"rendered":"\n\n\n
\"\"<\/td>\nMy paper with Alfonso Tortorell on higher versions of Kirillov’s local Lie algebras has now been published in Diffrential Geometry and Applications [1]. If you have access to this journal you can follow this link<\/a>. <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In this paper we take the point of view that Jacobi geometry is best understood as homogeneous Poisson geometry <\/a>– that is Poisson geometry on principle <\/a>\\(\\mathbb{R}^{\\times}\\)-bundles. Every line bundle over a manifold can be understood in terms of such a principle bundle.<\/p>\n

The same holds try when we pass to supermanifolds. With this in mind Alfonso and I more-or-less just replace Poisson with higher or homotopy Poisson. This allows us to neatly define an \\(L_{\\infty}\\)-algebra <\/a>on the space of sections of an even line bundle in the categeory of supermanifolds. This algebra is the higher\/homotopy generalisation of Kirillov’s local Lie algebra on the space of sections of a line bundle. <\/p>\n

We show that the basic theorems from Kirillov’s local Lie algebras or Jacobi bundles all passes to this higher case.<\/p>\n

Refrences<\/strong>
\n[1] Andrew James Bruce & Alfonso Giuseppe Tortorella, Kirillov structures up to homotopy, Differential Geometry and its Applications Volume 48, October 2016, Pages 72\u201386.<\/p>\n","protected":false},"excerpt":{"rendered":"

My paper with Alfonso Tortorell on higher versions of Kirillov’s local Lie algebras has now been published in Diffrential Geometry and Applications [1]. If you have access to this journal you can follow this link. In this paper we take the point of view that Jacobi geometry is best understood as homogeneous Poisson geometry – … Continue reading Kirillov structures up to homotopy<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,13],"tags":[],"class_list":["post-5131","post","type-post","status-publish","format-standard","hentry","category-post-doc-poland","category-research-work"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5131","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/comments?post=5131"}],"version-history":[{"count":6,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5131\/revisions"}],"predecessor-version":[{"id":5137,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/5131\/revisions\/5137"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=5131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=5131"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=5131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}