On the symmetric enveloping algebra of planar algebra subfactors
Stephen Curran, Vaughan F. R. Jones, Dimitri Shlyakhtenko
TL;DR
This paper provides a diagrammatic approach to symmetric enveloping algebras of planar algebra subfactors, introduces derivations, and computes related free entropy dimensions, advancing understanding of their algebraic and entropy properties.
Contribution
It offers a new diagrammatic description of symmetric enveloping algebras and constructs derivations, with entropy dimension calculations, enhancing the analysis of planar algebra subfactors.
Findings
Diagrammatic description of symmetric enveloping algebras
Construction of natural derivations on these factors
Calculation of a free entropy dimension type quantity
Abstract
We give a diagrammatic description of Popa's symmetric enveloping algebras associated to planar algebra subfactors. As an application we construct a natural family of derivations on these factors, and compute a certain free entropy dimension type quantity.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Random Matrices and Applications