{"id":5777,"date":"2026-02-20T04:39:59","date_gmt":"2026-02-19T20:39:59","guid":{"rendered":"https:\/\/transactions.nast.ph\/?p=5777"},"modified":"2026-03-26T14:53:39","modified_gmt":"2026-03-26T06:53:39","slug":"commutative-centralizer-algebras-and-related-structures","status":"publish","type":"post","link":"https:\/\/transactions.nast.ph\/?p=5777","title":{"rendered":"Commutative Centralizer Algebras and Related Structures"},"content":{"rendered":"\n<p class=\"has-text-align-center\">Jose Maria P. Balmaceda<br>Department of Mathematics, College of Science<br>University of the Philippines Diliman<\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"http:\/\/doi.org\/10.57043\/transnastphl.1999.5777\">http:\/\/doi.org\/10.57043\/transnastphl.1999.5777<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-1 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p><strong>Abstract<\/strong><\/p>\n\n\n\n<p>Let M (x) be a completely reducible matrix representation of a group Gover a field K. The set C (M) of matrices T over K such that TM (x) = M (x)T for all x E G forms an algebra over K called the centralizer algebra of M. In this paper we investigate the centralizer algebras of permutation representations. We prove a sufficiency condition for the commutativity of centralizer algebras of semi-direct products and also obtain several commutativity results coming from some classes of finite groups using character theory and other techniques. Finally we show how these algebras arise in various contexts and discuss some related structures.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h5 class=\"wp-block-heading\">Keywords<\/h5>\n\n\n<div class=\"taxonomy-post_tag wp-block-post-terms\"><a href=\"https:\/\/transactions.nast.ph\/?tag=bose-mesner-algebra\" rel=\"tag\">Bose Mesner algebra<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=centralizer-algeba\" rel=\"tag\">centralizer algeba<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=group-algebra\" rel=\"tag\">group algebra<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=hecke-algebra\" rel=\"tag\">Hecke algebra<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=permutation-character\" rel=\"tag\">permutation character<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=representation\" rel=\"tag\">representation<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/transactions.nast.ph\/?tag=symmetric-group\" rel=\"tag\">symmetric group<\/a><\/div><\/div>\n<\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\"  class=\"wp-block-file__embed\" data=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_7_Commutative-Centralizer-Algebras-and-Related-Structures.pdf\" type=\"application\/pdf\" style=\"width:100%;height:1090px\" aria-label=\"Embed of TNP 1999 (21)_7_Commutative Centralizer Algebras and Related Structures.\"><\/object><a id=\"wp-block-file--media-a7f4625b-6fdf-4f14-8615-29719e8c80bc\" href=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_7_Commutative-Centralizer-Algebras-and-Related-Structures.pdf\">TNP 1999 (21)_7_Commutative Centralizer Algebras and Related Structures<\/a><a href=\"https:\/\/transactions.nast.ph\/wp-content\/uploads\/2026\/02\/TNP-1999-21_7_Commutative-Centralizer-Algebras-and-Related-Structures.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a7f4625b-6fdf-4f14-8615-29719e8c80bc\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Jose Maria P. Balmaceda<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[819],"tags":[866,868,869,864,867,865,870],"class_list":{"0":"post-5777","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-1999-technical-papers","7":"tag-bose-mesner-algebra","8":"tag-centralizer-algeba","9":"tag-group-algebra","10":"tag-hecke-algebra","11":"tag-permutation-character","12":"tag-representation","13":"tag-symmetric-group","14":"czr-hentry"},"_links":{"self":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5777"}],"collection":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5777"}],"version-history":[{"count":3,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5777\/revisions"}],"predecessor-version":[{"id":6047,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=\/wp\/v2\/posts\/5777\/revisions\/6047"}],"wp:attachment":[{"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/transactions.nast.ph\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}