{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T13:27:16Z","timestamp":1775827636524,"version":"3.50.1"},"reference-count":19,"publisher":"Canadian Mathematical Society","issue":"4","license":[{"start":{"date-parts":[[2018,11,20]],"date-time":"2018-11-20T00:00:00Z","timestamp":1542672000000},"content-version":"unspecified","delay-in-days":4737,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Can. math. bull."],"published-print":{"date-parts":[[2005,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500002897_inline1\"\/> be the positive part of the quantized enveloping algebra <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500002897_inline2\"\/>. Using results of Alev\u2013Dumas and Caldero related to the center of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500002897_inline1\"\/>, we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra <jats:italic>U<\/jats:italic>(g) of a complex semisimple Lie algebra g, and also of an analogous result of Joseph\u2013Letzter for the quantum algebra <jats:italic>\u016c<jats:sub>q<\/jats:sub><\/jats:italic>(g). Of greater importance to its representation theory is the fact that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500002897_inline1\"\/> is free over a larger polynomial subalgebra <jats:italic>N<\/jats:italic> in <jats:italic>n<\/jats:italic> variables. Induction from <jats:italic>N<\/jats:italic> to <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0008439500002897_inline1\"\/> provides infinite-dimensional modules with good properties, including a grading that is inherited by submodules.<\/jats:p>","DOI":"10.4153\/cmb-2005-054-8","type":"journal-article","created":{"date-parts":[[2010,12,7]],"date-time":"2010-12-07T23:25:35Z","timestamp":1291764335000},"page":"587-600","source":"Crossref","is-referenced-by-count":2,"title":["Separation of Variables for"],"prefix":"10.4153","volume":"48","author":[{"given":"Samuel A.","family":"Lopes","sequence":"first","affiliation":[]}],"member":"2643","published-online":{"date-parts":[[2018,11,20]]},"reference":[{"key":"S0008439500002897_ref019","doi-asserted-by":"publisher","DOI":"10.2977\/prims\/1195173355"},{"key":"S0008439500002897_ref017","first-page":"51","article-title":"PBW-bases of quantum groups","volume":"470","author":"Ringel","year":"1996","journal-title":"J. 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