• Corpus ID: 222209084

# Classification of Thompson related groups arising from Jones technology I

@article{Brothier2020ClassificationOT,
title={Classification of Thompson related groups arising from Jones technology I},
author={Arnaud Brothier},
journal={arXiv: Group Theory},
year={2020}
}
In the quest in constructing conformal field theories (CFT) Jones has discovered a beautiful and deep connection between CFT, Richard Thompson's groups and knot theory. This led to a powerful framework for constructing actions of particular groups arising from categories such as Richard Thompson's groups and braid groups. In particular, given a group and two of its endomorphisms one can construct a semidirect product. Those semidirect products have remarkable diagrammatic descriptions which…
2 Citations
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We introduce “braided” versions of self-similar groups and Röver–Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu,

## References

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Irreducibility of the Wysiwyg Representations of Thompson’s Groups
• V. Jones
• Mathematics
Representation Theory, Mathematical Physics, and Integrable Systems
• 2021
We prove irreducibility and mutual inequivalence for certain unitary representations of R. Thompson's groups F and T.
On closed subgroups of the R. Thompson group $F$.
• Mathematics
• 2021
We prove that Thompson's group $F$ has a subgroup $H$ such that the conjugacy problem in $H$ is undecidable and the membership problem in $H$ is easily decidable. The subgroup $H$ of $F$ is a closed
Classification of thompson related groups arising from Jones technology I
• 2020
On the Alexander theorem for the oriented Thompson group F
In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$. In this paper we prove, by analogy with
Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Mathematics
• 2019
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory
Haagerup property for wreath products constructed with Thompson's groups
Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the
Jones Representations of Thompson’s Group F Arising from Temperley–Lieb–Jones Algebras
• Mathematics
International Mathematics Research Notices
• 2019
Following a procedure due to Jones, using suitably normalized elements in a Temperley–Lieb–Jones (planar) algebra, we introduce a 3-parametric family of unitary representations of the Thompson’s
On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots
Surprisingly Richard Thompson's groups have recently appeared in Jones' subfactor theory. Vaughan Jones is famous for linking theories that are a priori completely disconnected; for instance, his
On Jones’ connections between subfactors
• conformal field theory, Thompson’s groups and knots. to appear in Celebratio Mathematica, Preprint
• 2019
On the Construction of Knots and Links from Thompson’s Groups
• V. Jones
• Mathematics
Knots, Low-Dimensional Topology and Applications
• 2019
We review recent developments in the theory of Thompson group representations related to knot theory.