Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras
| dc.creator | Mason, Geoffrey | |
| dc.creator | Ng, Siu-Hung | |
| dc.date | 2003-03-18 | |
| dc.date | 2003-04-29 | |
| dc.date.accessioned | 2026-07-07T04:56:08Z | |
| dc.date.available | 2026-07-07T04:56:08Z | |
| dc.description | In this paper, we obtain a canonical central element $ν_H$ for each semi-simple quasi-Hopf algebra $H$ over any field $k$ and prove that $ν_H$ 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 $χ$, $χ(ν_H)$ 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 $χ(ν_H)$ 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 $χ(ν_H)$, and certain associated bilinear forms when the underlying field $k$ is algebraically closed of characteristic zero. | |
| dc.description | 32 pages (version 3) | |
| dc.identifier | https://arxiv.org/abs/math/0303213 | |
| dc.identifier | http://arxiv.org/abs/math/0303213 | |
| dc.identifier | Adv. Math. 190 (2005) no. 1, 161--195 | |
| dc.identifier | doi:10.1016/j.aim.2003.12.004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66816 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 16W30; 16G10 | |
| dc.title | Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras | |
| dc.type | text |