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Subfactor; standard invariant; planar algebra; Hopf algebra; Kac algebra

We obtain (two equivalent) presentations — in terms of generators and relations — of the planar algebra associated with the subfactor corresponding to (an outer action on a factor by) a finite-dimensional Kac algebra. One of the relations shows that the antipode of the Kac algebra agrees with the ‘rotation on 2-boxes’.

Vijay Kodiyalam¹ Zeph Landau² V S Sunder¹

1. The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai - 600 113, India
2. University of California, Berkeley, CA - 94720, USA

Published

February 2003

Manuscript received

13 November 2001

Manuscript revised

15 June 2002