From subfactor planar algebras to subfactors
Vijay Kodiyalam, V. S. Sunder
TL;DR
This paper provides a purely planar algebraic proof connecting subfactor planar algebras to the construction of extremal subfactors, clarifying the relationship between these algebraic structures.
Contribution
It offers a new, purely planar algebraic proof of a key result linking subfactor planar algebras to extremal subfactors, simplifying previous approaches.
Findings
Established a planar algebraic proof of the Guionnet-Jones-Shlaykhtenko construction
Confirmed the correspondence between subfactor planar algebras and extremal subfactors
Enhanced understanding of the algebraic foundations of subfactor theory
Abstract
We present a purely planar algebraic proof of the main result of a paper of Guionnet-Jones-Shlaykhtenko which constructs an extremal subfactor from a subfactor planar algebra whose standard invariant is given by that planar algebra.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models