An analogue of Radford's S^4 formula for finite tensor categories
| dc.creator | Etingof, Pavel | |
| dc.creator | Nikshych, Dmitri | |
| dc.creator | Ostrik, Viktor | |
| dc.date | 2004-04-27 | |
| dc.date.accessioned | 2026-07-07T13:16:06Z | |
| dc.date.available | 2026-07-07T13:16:06Z | |
| dc.description | We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors ?^{**} and D tensor ^{**}? tensor D^{-1}. This provides a categorical generalization of D. Radford's S^4-formula for finite dimensional Hopf algebras and its generalizations for weak Hopf algebras and for quasi-Hopf algebras, and conjectured in general in \cite{EO}. When C is braided, we establish a connection between the above isomorphism and the Drinfeld isomorphism of C. We also show that a factorizable braided tensor category is unimodular (i.e., D=1). Finally, we apply our theory to prove that the pivotalization of a fusion category is spherical, and give a purely algebraic characterization of exact module categories. | |
| dc.description | 14 pages, AMS-Latex | |
| dc.identifier | https://arxiv.org/abs/math/0404504 | |
| dc.identifier | http://arxiv.org/abs/math/0404504 | |
| dc.identifier | International Mathematics Research Notices 54 (2004), 2915--2933. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230681 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Category Theory | |
| dc.title | An analogue of Radford's S^4 formula for finite tensor categories | |
| dc.type | text |