{"id":156,"date":"2021-04-13T11:48:27","date_gmt":"2021-04-13T10:48:27","guid":{"rendered":"http:\/\/blogs.cardiff.ac.uk\/mathsugprojects\/?p=156"},"modified":"2022-11-11T10:24:53","modified_gmt":"2022-11-11T10:24:53","slug":"representation-theory-of-finite-groups-dr-m-pugh","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/representation-theory-of-finite-groups-dr-m-pugh\/","title":{"rendered":"Representation Theory of Finite Groups &#8211; Supervisor: Dr. M. Pugh"},"content":{"rendered":"<p style=\"color: #383735\"><strong>Title of project:<\/strong><br \/>\nRepresentation Theory Of Finite Groups<\/p>\n<p style=\"color: #383735\"><strong>Code:<\/strong><br \/>\nMP2122A<\/p>\n<p style=\"color: #383735\"><strong>Supervisor:&nbsp;<\/strong><br \/>\nDr. M. Pugh<\/p>\n<p><strong>Project description:<\/strong><br \/>\nIn the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces. In particular, group elements can be represented as matrices so that the group operation can be represented by matrix multiplication. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra.<br \/>\nThe main task of this project will be to classify (real and complex) representations of the dihedral and cyclic groups.<br \/>\n<strong style=\"color: #383735\">Project offered as double module, single module, or both:<\/strong><br \/>\nDouble<\/p>\n<p style=\"color: #383735\"><strong>Prerequisite 2nd year modules:<\/strong><\/p>\n<p>MA2013 Groups<\/p>\n<p style=\"color: #383735\"><strong>Recommended 3rd year module for concurrent study:<\/strong><\/p>\n<p style=\"color: #383735\">MA3013 Rings and Fields<\/p>\n<p style=\"color: #383735\"><strong>Number of students who can be supervised on this project:<\/strong><\/p>\n<p style=\"color: #383735\">1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title of project: Representation Theory Of Finite Groups Code: MP2122A Supervisor:&nbsp; Dr. M. Pugh Project description: In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces. In particular, group elements can be represented as matrices so that the group operation can be represented by matrix &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/representation-theory-of-finite-groups-dr-m-pugh\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Representation Theory of Finite Groups &#8211; Supervisor: Dr. M. Pugh<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2,4,7],"tags":[],"class_list":["post-156","post","type-post","status-publish","format-standard","hentry","category-2021-2022","category-double","category-yr-3-descriptions-2021-2022"],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/156","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/comments?post=156"}],"version-history":[{"count":5,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/156\/revisions"}],"predecessor-version":[{"id":2021,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/156\/revisions\/2021"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/media?parent=156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/categories?post=156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/tags?post=156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}