2003/03/31 by Geoffrey Mason, Siu‐Hung Ng, Siu-Hung Ng · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #math.RT #msc:16G10 #msc:16W30
paper · pdf · doi:10.1016/j.aim.2003.12.004
published as Adv. Math. 190 (2005) no. 1, 161--195 · 32 pages (version 3)
arxiv created 2003/04/29 · openalex publication_date 2004/03/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we obtain a canonical central element νH for each semi-simple quasi-Hopf algebra H over any field k and prove that νH is invariant under gauge transformations. We show that if k is algebraically closed of characteristic zero then for any irreducible representation of H which affords the character χ, χ(νH) takes only the values 0, 1 or -1, moreover if H is a Hopf algebra or a twisted quantum double of a finite group then χ(νH) is the corresponding Frobenius-Schur Indicator. We also prove an analog of a Theorem of Larson-Radford for split semi-simple quasi-Hopf algebra over any field k. Using this result, we establish the relationship between the antipode S, the values of χ(νH), and certain associated bilinear forms when the underlying field k is algebraically closed of characteristic zero.