On Jones' planar algebras

Kodiyalam, Vijay ; Sunder, V. S. (2004) On Jones' planar algebras Journal of Knot Theory and Its Ramifications, 13 (2). pp. 219-247. ISSN 0218-2165

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Official URL: http://www.worldscinet.com/jktr/13/1302/S021821650...

Related URL: http://dx.doi.org/10.1142/S021821650400310X


We show that a certain natural class of tangles 'generate the collection of all tangles with respect to composition'. This result is motivated by, and describes the reasoning behind, the 'uniqueness assertion' in Jones' theorem on the equivalence between extremal subfactors of finite index and what we call 'subfactor planar algebras' here. This result is also used to identify the manner in which the planar algebras corresponding to M⊂M1 and Nop⊂Mop are obtained from that of N⊂M. Our results also show that 'duality' in the category of extremal subfactors of finite index extends naturally to the category of 'general' planar algebras (not necessarily finite-dimensional or spherical or connected or C, in the terminology of Jones).

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
Keywords:Planar Tangles; Generating Sets; Subfactors
ID Code:53551
Deposited On:09 Aug 2011 11:52
Last Modified:18 May 2016 06:38

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