{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:19Z","timestamp":1760243719365,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2012,10,5]],"date-time":"2012-10-05T00:00:00Z","timestamp":1349395200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Motivated by the orthogonality relations for irreducible characters of a finite group, we evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements. We then discuss results for products of skew-primitive elements. Examples include groups, (quantum groups over) Lie algebras, the small quantum groups of Lusztig, and their variations (by Andruskiewitsch and Schneider).<\/jats:p>","DOI":"10.3390\/axioms1030259","type":"journal-article","created":{"date-parts":[[2012,10,5]],"date-time":"2012-10-05T13:51:07Z","timestamp":1349445067000},"page":"259-290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Sum of a Finite Group of Weights of a Hopf Algebra"],"prefix":"10.3390","volume":"1","author":[{"given":"Apoorva","family":"Khare","sequence":"first","affiliation":[{"name":"Department of Mathematics and Department of Statistics, Stanford University, 390 Serra Mall, Stanford, CA 94305, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,10,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.2307\/2373888","article-title":"The order of the antipode of a finite-dimensional Hopf algebra is finite","volume":"98","author":"Radford","year":"1976","journal-title":"Am. 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Groups and Representations, Springer-Verlag.","DOI":"10.1007\/978-1-4612-0799-3"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1006\/aima.1994.1049","article-title":"Integration of quantum many-body problems by affine knizhnik-zamolodchikov equations","volume":"106","author":"Cherednik","year":"1994","journal-title":"Adv. Math."},{"key":"ref_17","unstructured":"Knuth, D.E. (1997). The Art of Computer Programming, Volume 1: Fundamental Algorithms, Addison-Wesley."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/1\/3\/259\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:52:41Z","timestamp":1760219561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/1\/3\/259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,5]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,12]]}},"alternative-id":["axioms1030259"],"URL":"https:\/\/doi.org\/10.3390\/axioms1030259","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2012,10,5]]}}}