On Jones Subgroup of R. Thompson's Group T

2017/10/19 by Jordan Nikkel, Yunxiang Ren, Nikkel, Jordan +1 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1710.06972

Abstract

Jones introduced unitary representations for the Thompson groups F and T from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups F and T. Golan and Sapir studied F and identified it as a copy of the Thompson group F₃. In this paper we completely describe T and show that T coincides with its commensurator in T, implying that the corresponding unitary representation is irreducible. We also generalize the notion of the Stallings 2-core for diagram groups to T, showing that T and T₃ are not isomorphic, but as annular diagram groups they have very similar presentations.

Cited by

• Thompson's Group V and Virtual Link Theory
• On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots

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