Affine modules and the drinfeld center

Authors

Paramita Das, Indian Statistical Institute, Kolkata
Shamindra Kumar Ghosh, Indian Statistical Institute, Kolkata
Ved Prakash Gupta, Jawaharlal Nehru University

Article Type

Research Article

Publication Title

Mathematica Scandinavica

Abstract

Given a finite index subfactor, we show that the affine morphisms at zero level in the affine category over the planar algebra associated to the sub factor is isomorphic to the fusion algebra of the subfactor as a ∗-aIgebra. This identification paves the way to analyze the structure of affine P-modules with weight zero for any subfactor planar algebra P (possibly having infinite depth). Further, for irreducible depth two subfactor planar algebras, we establish an additive equivalence between the category of affine P-moduIes and the center of the category of N-N-bimodules generated by L2(M); this partially verifies a conjecture of Jones and Walker.

First Page

119

Last Page

151

DOI

10.7146/math.scand.a-23301

Publication Date

1-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Das, Paramita; Ghosh, Shamindra Kumar; and Gupta, Ved Prakash, "Affine modules and the drinfeld center" (2016). Journal Articles. 4086.
https://digitalcommons.isical.ac.in/journal-articles/4086