A Construction of Subfactors of Planar Algebra
Wunghun Ri, Gwangho Jong
TL;DR
This paper introduces a new planar algebraic method for constructing subfactors, expanding on existing frameworks by utilizing fundamental planar algebra concepts like involution and conditional expectation.
Contribution
It provides a novel construction approach for subfactors directly from planar algebra concepts, enhancing the understanding of their algebraic structure.
Findings
New construction method for subfactors from planar algebra concepts
Generalizes previous approaches by Guionet-Jones-Shlyakhtenko-Walker and Kodiyalam-Sunder
Demonstrates the effectiveness of using involution, inclusion, and expectation in subfactor construction
Abstract
We present more planar algebraic construction of subfactors than those of Guionet-Jones-Shlyakhtenko-Walker and Kodiyalam-Sunder which start from a subfactor planar algebra and give in a direct way a subfactor of the same standard invariant with the planar algebra. Our construction is based on using the ordinary concepts in planar algebras such as involution, inclusion and conditional expectation mappings as it is
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models