{"id":2801,"date":"2013-01-04T14:09:27","date_gmt":"2013-01-04T13:09:27","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/ajb\/?p=2801"},"modified":"2013-01-04T14:09:27","modified_gmt":"2013-01-04T13:09:27","slug":"brackets-by-janusz-grabowski","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/ajb\/2013\/01\/04\/brackets-by-janusz-grabowski\/","title":{"rendered":""Brackets" by Janusz Grabowski"},"content":{"rendered":"

Prof. Grabowski has placed a review of the various brackets found in geometry and physics [1]. He also covers some of the ideas of superalgebra and graded differential geometry as many of the brackets really have their roots there. The review is based on a mini-course held at XXI Fall Workshops on Geometry and Physics, Burgos (Spain), 2012.<\/p>\n

I have posted here about the review here as it contains a lot of the background material needed to understand my own research. In particular I am interested in brackets found in supergeometry, including super versions of Poisson, Jacobi and Loday brackets.<\/p>\n

Brackets?<\/strong><\/p>\n

Rather generally, a bracket is understood as a non-associative operation on a vector space or a module. The principle example here is a Lie bracket<\/a>. The review focuses on Lie brackets, such as Poisson and Jacobi brackets as well as Loday brackets, which are a non-skewsymmetric generalisation of a Lie bracket.<\/p>\n

Interestingly, various forms of brackets arise in a wide context in contemporary mathematics. For example, Poisson brackets are found in classical and quantum mechanics as well as the theory of cluster algebras<\/a> and geometric representation theory<\/a>.<\/p>\n

Prof. Janusz Grabowski<\/strong><\/p>\n\n\n\n
\n\"Grabowski\"<\/td>\n\n

Prof Grabowski is Head of the Department of Mathematical Physics and Differential Geometry at the Institute of Mathematics within Polish Academy of Sciences.<\/p>\n

His personal homepage can be found here<\/a>.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Reference<\/strong><\/p>\n

[1] Janusz Grabowski, Brackets, arXiv:1301.0227 [math.DG<\/a>], 2012.<\/p>\n","protected":false},"excerpt":{"rendered":"

Prof. Grabowski has placed a review of the various brackets found in geometry and physics [1]. He also covers some of the ideas of superalgebra and graded differential geometry as many of the brackets really have their roots there. The review is based on a mini-course held at XXI Fall Workshops on Geometry and Physics, … Continue reading "Brackets" by Janusz Grabowski<\/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":[6,13],"tags":[],"class_list":["post-2801","post","type-post","status-publish","format-standard","hentry","category-general-mathematics","category-research-work"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/2801","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=2801"}],"version-history":[{"count":0,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/posts\/2801\/revisions"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/media?parent=2801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/categories?post=2801"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/ajb\/wp-json\/wp\/v2\/tags?post=2801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}