{"ddc":["510"],"year":"2022","bi_doctype":"bi_dissertation","type_old":["dissertation","biDissertation","bidissertation","bi_dissertation"],"first_contributor":"Hansper, Ulrike","locked":"1","publisher":"Universität Bielefeld","email":"ulrike.hansper@web.de","status":"public","title":"Classification of the indecomposable finite dimensional modules of clannish algebras","type":"bi_dissertation","file_date_updated":"2022-05-15T08:49:28Z","language":[{"iso":"eng"}],"_id":"2962952","author":[{"last_name":"Hansper","department":[{"_id":"10020"}],"first_name":"Ulrike","full_name":"Hansper, Ulrike","id":"87070984"}],"unibi_person":1,"oa":1,"date_updated":"2022-05-18T14:40:48Z","date_created":"2022-05-15T09:02:16Z","department":[{"_id":"10020"}],"place":"Bielefeld","abstract":[{"lang":"eng","text":"In this thesis we classify all indecomposable finite dimensional modules of\r\nclannish algebras with idempotent relations on the special loops. To this\r\nend, we start with the introduction of the notion of asymmetric and symmetric\r\nstrings and bands in terms of words. The classification will be given\r\nin terms of those. We first examine directions on special letters in these\r\nwords of a clannish algebra. Then we reduce the case to skewed-gentle algebras\r\nand construct a bundle of semichains for such an algebra. Thus, we\r\nare able to reduce the classification problem for skewed-gentle algebras to\r\nthe matrix problem of bundles of semichains studied by Bondarenko. From\r\nthis problem, we extract one classification of the indecomposable finite dimensional\r\nmodules of a skewed-gentle algebra. From this classification, we\r\ncan deduce a classification for clannish algebras. Finally, we adjust this classification to obtain one similar to that obtained by Crawley-Boevey, in which\r\nthe symmetric band modules are indexed by a vector space equipped with a\r\npair of idempotent endomorphisms. In contrast to Crawley-Boevey's classification, however, ours gives representations with better bases, not requiring\r\nthe introduction of a fixed non-zero non-identity element of the field, and so\r\nworking over the field with two elements. Applied to the algebra generated\r\nby an idempotent and a square zero element, it confirms a conjecture of\r\nCrawley-Boevey in 1988."}],"license":"https://creativecommons.org/licenses/by/4.0/","page":"287","file":[{"checksum":"6e3b5062e0bd660fcfe1fe50aacc1b51","relation":"main_file","date_created":"2022-05-15T08:49:28Z","file_name":"Thesis_UH_15042022.pdf","date_updated":"2022-05-15T08:49:28Z","file_size":1494855,"file_id":"2962953","content_type":"application/pdf","access_level":"open_access"}],"doi":"10.4119/unibi/2962952","citation":{"apa_indent":"<div style=\"text-indent:-25px; padding-left:25px;padding-bottom:0px;\">Hansper, U. (2022).  <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld. <a href=\"https://doi.org/10.4119/unibi/2962952\" target=\"_blank\">https://doi.org/10.4119/unibi/2962952</a></div>","bio1":"Hansper U (2022) <br /><em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>.<br />Bielefeld: Universität Bielefeld.","wels":"Hansper, U. (2022): Classification of the indecomposable finite dimensional modules of clannish algebras. Bielefeld: Universität Bielefeld.","ieee":" U. Hansper, <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>,  Bielefeld: Universität Bielefeld, 2022.","chicago":"<div style=\"text-indent:-25px; padding-left:25px;padding-bottom:0px;\">Hansper, Ulrike. 2022. <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld.</div>","default":"Hansper U (2022) <br />Bielefeld: Universität Bielefeld.","ama":"Hansper U. <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld; 2022.","angewandte-chemie":"U.  Hansper, <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>, Universität Bielefeld, Bielefeld, <strong>2022</strong>.","mla":"Hansper, Ulrike. <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld, 2022.","apa":"Hansper, U. (2022).  <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld. <a href=\"https://doi.org/10.4119/unibi/2962952\" target=\"_blank\">https://doi.org/10.4119/unibi/2962952</a>","lncs":" Hansper, U.: Classification of the indecomposable finite dimensional modules of clannish algebras. Universität Bielefeld, Bielefeld (2022).","frontiers":"Hansper, U. (2022). Classification of the indecomposable finite dimensional modules of clannish algebras. Bielefeld: Universität Bielefeld.","harvard1":"Hansper, U., 2022. <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>, Bielefeld: Universität Bielefeld.","dgps":"<div style=\"text-indent:-25px; padding-left:25px;padding-bottom:0px;\">Hansper, U. (2022). <em>Classification of the indecomposable finite dimensional modules of clannish algebras</em>. Bielefeld: Universität Bielefeld. doi:10.4119/unibi/2962952.</div>"},"user_id":"89573","defense_date":"2022-04-11","supervisor":[{"last_name":"Crawley-Boevey","full_name":"Crawley-Boevey, William Walstan","id":"80749906","first_name":"William Walstan"}],"urn":"urn:nbn:de:0070-pub-29629527"}