{"id":542,"date":"2017-12-03T16:02:08","date_gmt":"2017-12-03T14:02:08","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=542"},"modified":"2017-12-03T16:02:08","modified_gmt":"2017-12-03T14:02:08","slug":"the-centralizer-of-k-in-ugotimes-cp-for-the-group-so_e41","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/the-centralizer-of-k-in-ugotimes-cp-for-the-group-so_e41\/","title":{"rendered":"The centralizer of \"K\" in \"U(g)\otimes C(p)\" for the group \"SO_e(4,1)\""},"content":{"rendered":"

<\/p>\n

Author: Ana Prli\u0107<\/strong><\/p>\n

Glasnik Matemati\u010dki<\/a>, Vol. 52, No. 2 (2017), 275-288.<\/h4>\n

DOI: 10.3336\/gm.52.2.07<\/p>\n

Abstract.<\/b>\u00a0Let \"G\" be the Lie group \"SO_e(4,1)\", with maximal compact subgroup \"K = S(O(4) \times O(1))_e\cong SO(4)\". Let \"\mathfrak{g}=\mathfrak{so}(5,\mathbb{C})\" be the complexification of the Lie algebra \"\mathfrak{g}_0 = \mathfrak{so}(4,1)\" of \"G\", and let \"U(\mathfrak{g})\" be the universal enveloping algebra of \"\mathfrak{g}\". Let \"\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}\" be the Cartan decomposition of \"\mathfrak{g}\", and \"C(\mathfrak{p})\" the Clifford algebra of \"\mathfrak{p}\" with respect to the trace form \"B(X, Y) = \text{tr}(XY)\" on \"\mathfrak{p}\". In this paper we give explicit generators of the algebra \"(U(\mathfrak{g}) \otimes C(\mathfrak{p}))^{K}\".<\/p>\n

2010 Mathematics Subject Classification.<\/b>\u00a0\u00a0 22E47, 22E46.<\/p>\n

Key words and phrases.<\/b>\u00a0\u00a0 Lie group, Lie algebra, representation, Dirac operator, Dirac cohomology.<\/p>","protected":false},"excerpt":{"rendered":"

Author: Ana Prli\u0107 Glasnik Matemati\u010dki, Vol. 52, No. 2 (2017), 275-288. DOI: 10.3336\/gm.52.2.07 Abstract.\u00a0Let be the Lie group , with maximal compact subgroup . Let be the complexification of the Lie algebra of , and let be the universal enveloping algebra of . Let be the Cartan decomposition of , […]<\/a><\/p>\n<\/div>","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[18,14],"tags":[],"_links":{"self":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/542"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/comments?post=542"}],"version-history":[{"count":5,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/542\/revisions"}],"predecessor-version":[{"id":547,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/542\/revisions\/547"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=542"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}