{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:58Z","timestamp":1747198078578,"version":"3.40.5"},"reference-count":41,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/04721\/2013","UIDB\/04721\/2020","PB\/BD\/113633\/2015"],"award-info":[{"award-number":["UID\/MAT\/04721\/2013","UIDB\/04721\/2020","PB\/BD\/113633\/2015"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The supercharacter theory of a finite group was introduced by Diaconis and Isaacs as an alternative to the usual irreducible character theory, and illustrated with a construction in the case of finite algebra groups. We extend this construction to arbitrary countable discrete algebra groups, where superclasses and indecomposable supercharacters play the role of conjugacy classes and indecomposable characters, respectively.\nHowever, we adopt an ergodic theoretical point of view. The theory is then illustrated with a characterization of standard supercharacters of the group of upper unitriangular matrices over an algebraically closed field of prime characteristic.<\/jats:p>","DOI":"10.1515\/forum-2022-0220","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T15:58:26Z","timestamp":1666713506000},"page":"221-244","source":"Crossref","is-referenced-by-count":1,"title":["Supercharacters of discrete algebra groups"],"prefix":"10.1515","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1907-657X","authenticated-orcid":false,"given":"Carlos A.\u2009M.","family":"Andr\u00e9","sequence":"first","affiliation":[{"name":"Centro de An\u00e1lise Funcional, Estruturas Lineares e Aplica\u00e7\u00f5es (Grupo de Estruturas Lineares e Combinat\u00f3rias) , Departamento de Matem\u00e1tica , Faculdade de Ci\u00eancias , Universidade de Lisboa , Campo Grande, Edif\u00edcio C6, Piso 2, 1749-016 Lisboa , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3276-4569","authenticated-orcid":false,"given":"Jocelyn","family":"Lochon","sequence":"additional","affiliation":[{"name":"Centro de An\u00e1lise Funcional, Estruturas Lineares e Aplica\u00e7\u00f5es (Grupo de Estruturas Lineares e Combinat\u00f3rias) , Departamento de Matem\u00e1tica , Faculdade de Ci\u00eancias , Universidade de Lisboa , Campo Grande, Edif\u00edcio C6, Piso 2, 1749-016 Lisboa , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2022,10,26]]},"reference":[{"key":"2024082608194674855_j_forum-2022-0220_ref_001","doi-asserted-by":"crossref","unstructured":"E. M.  Alfsen,\nCompact Convex Sets and Boundary Integrals,\nErgeb. Math. Grenzgeb. (3) 57,\nSpringer, New York, 1971.","DOI":"10.1007\/978-3-642-65009-3"},{"key":"2024082608194674855_j_forum-2022-0220_ref_002","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9,\nBasic characters of the unitriangular group,\nJ. Algebra 175 (1995), no. 1, 287\u2013319.","DOI":"10.1006\/jabr.1995.1187"},{"key":"2024082608194674855_j_forum-2022-0220_ref_003","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9,\nBasic sums of coadjoint orbits of the unitriangular group,\nJ. Algebra 176 (1995), no. 3, 959\u20131000.","DOI":"10.1006\/jabr.1995.1280"},{"key":"2024082608194674855_j_forum-2022-0220_ref_004","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9,\nThe regular character of the unitriangular group,\nJ. Algebra 201 (1998), no. 1, 1\u201352.","DOI":"10.1006\/jabr.1997.7258"},{"key":"2024082608194674855_j_forum-2022-0220_ref_005","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9,\nThe basic character table of the unitriangular group,\nJ. Algebra 241 (2001), no. 1, 437\u2013471.","DOI":"10.1006\/jabr.2001.8734"},{"key":"2024082608194674855_j_forum-2022-0220_ref_006","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9,\nBasic characters of the unitriangular group (for arbitrary primes),\nProc. Amer. Math. Soc. 130 (2002), no. 7, 1943\u20131954.","DOI":"10.1090\/S0002-9939-02-06287-1"},{"key":"2024082608194674855_j_forum-2022-0220_ref_007","unstructured":"C. A. M.  Andr\u00e9,\nSupercharacters of Unitriangular Groups and Set Partition Combinatorics,\nUniversidad Nacional de San Luis, San Luis, 2013;\nCIMPA school: \u201cModern Methods in Combinatorics ECOS2013\u201d (\u201c2da Escuela Puntana de Combinatoria: Escuela de Combinatoria del Sur\u201d)."},{"key":"2024082608194674855_j_forum-2022-0220_ref_008","doi-asserted-by":"crossref","unstructured":"C. A. M.  Andr\u00e9, F.  Gomes and J.  Lochon,\nIndecomposable supercharacters of the infinite unitriangular group,\nOperator Theory, Operator Algebras, and Matrix Theory,\nOper. Theory Adv. Appl. 267,\nBirkh\u00e4user\/Springer, Cham (2018), 1\u201324.","DOI":"10.1007\/978-3-319-72449-2_1"},{"key":"2024082608194674855_j_forum-2022-0220_ref_009","doi-asserted-by":"crossref","unstructured":"L. W.  Baggett, E.  Kaniuth and W.  Moran,\nPrimitive ideal spaces, characters, and Kirillov theory for discrete nilpotent groups,\nJ. Funct. 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Phelps,\nLectures on Choquet\u2019s Theorem, 2nd ed.,\nLecture Notes in Math. 1757,\nSpringer, Berlin, 2001.","DOI":"10.1007\/b76887"},{"key":"2024082608194674855_j_forum-2022-0220_ref_030","unstructured":"J.-P.  Pier,\nAmenable Locally Compact Groups,\nPure Appl. Math. (New York),\nJohn Wiley & Sons, New York, 1984."},{"key":"2024082608194674855_j_forum-2022-0220_ref_031","unstructured":"M.  Reed and B.  Simon,\nMethods of Modern Mathematical Physics. I, 2nd ed.,\nAcademic Press, New York, 1980."},{"key":"2024082608194674855_j_forum-2022-0220_ref_032","unstructured":"W.  Rudin,\nReal and Complex Analysis, 3rd ed.,\nMcGraw-Hill, New York, 1987."},{"key":"2024082608194674855_j_forum-2022-0220_ref_033","doi-asserted-by":"crossref","unstructured":"E.  Thoma,\n\u00dcber unit\u00e4re Darstellungen abz\u00e4hlbarer, diskreter Gruppen,\nMath. 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Soc. 109 (1963), 191\u2013220.","DOI":"10.1090\/S0002-9947-1963-0159923-5"},{"key":"2024082608194674855_j_forum-2022-0220_ref_038","doi-asserted-by":"crossref","unstructured":"A. M.  Vershik and S. V.  Kerov,\nAsymptotic theory of the characters of a symmetric group,\nFunct. Anal. Appl. 15 (1982), 246\u2013255.","DOI":"10.1007\/BF01106153"},{"key":"2024082608194674855_j_forum-2022-0220_ref_039","doi-asserted-by":"crossref","unstructured":"A. M.  Vershik and S. V.  Kerov,\nAsymptotic theory of the characters of a symmetric group,\nFunktsional. Anal. i Prilozhen. 15 (1981), no. 4, 15\u201327, 96.","DOI":"10.1007\/BF01106153"},{"key":"2024082608194674855_j_forum-2022-0220_ref_040","doi-asserted-by":"crossref","unstructured":"P.  Walters,\nAn Introduction to Ergodic Theory,\nGrad. Texts in Math. 79,\nSpringer, New York, 1982.","DOI":"10.1007\/978-1-4612-5775-2"},{"key":"2024082608194674855_j_forum-2022-0220_ref_041","unstructured":"N.  Yan,\nRepresentation theory of the finite unipotent linear groups,\nPh.D. thesis, University of Pennsylvania, (2001)."}],"container-title":["Forum Mathematicum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2022-0220\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2022-0220\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T08:21:38Z","timestamp":1724660498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/forum-2022-0220\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,26]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,5]]},"published-print":{"date-parts":[[2023,1,1]]}},"alternative-id":["10.1515\/forum-2022-0220"],"URL":"https:\/\/doi.org\/10.1515\/forum-2022-0220","relation":{},"ISSN":["0933-7741","1435-5337"],"issn-type":[{"type":"print","value":"0933-7741"},{"type":"electronic","value":"1435-5337"}],"subject":[],"published":{"date-parts":[[2022,10,26]]}}}