37 citations · 104 across the 27 of their papers we have counts for
33 papers
Representations of the infinite Cuntz algebra
David. E. Evans, Arnaud Brothier
We define an intrinsic unital completely positive (ucp) map from the Cuntz algebra to the Pythagorean with finitely many generators. This permits to lift states and cyclic represen…
The Cuntz-Pimsner algebra of the simplest Motzkin subproduct system is 2-subhomogeneous
Valeriano Aiello, Arnaud Brothier
The Motzkin subproduct system (SPS) is constructed from the Jones Wenzl idempotents of the Motzkin algebras, which generalizes the Temperley Lieb SPS. The simplest Motzkin SPS, whi…
A new perspective on spectra of quantum spaces
Arnaud Brothier
We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A toget…
Classification of representations of higher-rank graph C*-algebras
Arnaud Brothier, Aidan Sims, Dilshan Wijesena
We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Kr…
Moduli of representations of Leavitt path algebras
Arnaud Brothier, Dilshan Wijesena
We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its qui…
A tensor product for representations of the Cuntz algebra and of the R. Thompson groups
Arnaud Brothier, Dilshan Wijesena
The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups called Pythagorean. They all extend to the Cuntz algebra $…
Atomic representations of R. Thompson's groups and Cuntz's algebra
Arnaud Brothier, Dilshan Wijesena
We continue to study Pythagorean unitary representation of Richard Thompson's groups and their extension to the Cuntz(-Dixmier) algebra. Any linear isometry from a Hilbert…
Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra
Arnaud Brothier, Dilshan Wijesena
We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson grou…
Decomposition of Pythagorean representations of R. Thompson's groups
Arnaud Brothier, Dilshan Wijesena
We continue to study Pythagorean unitary representation of Richard Thompson's groups , and that are built from a single isometry from a Hilbert space to its double. By d…
Forest-skein groups II: construction from homogeneously presented monoids
Arnaud Brothier
Inspired by the reconstruction program of conformal field theories of Vaughan Jones we recently introduced a vast class of so called forest-skein groups. They are built from a skei…
Jones' representations of R. Thompson's groups not induced by finite-dimensional ones
Arnaud Brothier, Dilshan Wijesena
Given any linear isometry from a Hilbert space to its square one can explicitly construct a so-called Pythagorean unitary representation of Richard Thompson's group F. We introduce…
Forest-skein groups I: between Vaughan Jones' subfactors and Richard Thompson's groups
Arnaud Brothier
Vaughan Jones discovered unexpected connections between Richard Thompson's group and subfactor theory while attempting to construct conformal field theories (in short CFT). Among o…
Classification of Thompson related groups arising from Jones technology II
Arnaud Brothier
In this second article, we continue to study classes of groups constructed from a functorial method due to Vaughan Jones. A key observation of the author shows that these groups ha…
Classification of Thompson related groups arising from Jones technology I
Arnaud Brothier
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…
On Jones' connections between subfactors, conformal field theory, Thompson's groups and knots
Arnaud Brothier
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; fo…
Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
Arnaud Brothier, Alexander Stottmeister
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM) by operator-algebraic methods. The latter are based on Hamiltonian l…
Haagerup property for wreath products constructed with Thompson's groups
Arnaud Brothier
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…
Jones representations of Thompson's group arising from Temperley-Lieb-Jones algebras
Valeriano Aiello, Arnaud Brothier, Roberto Conti
Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations o…
Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups
Arnaud Brothier, Alexander Stottmeister
Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct 1+1-dimensional gauge theories on a spacetime cylinder. Given a separable compact group , we…
Pythagorean representations of Thompson's groups
Arnaud Brothier, Vaughan F. R. Jones
We introduce the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson's groups from representations of them. We calculate se…
On the Haagerup and Kazhdan properties of R. Thompson's groups
Arnaud Brothier, Vaughan F. R. Jones
A machine developed by the second author produces a rich family of unitary representations of the Thompson groups F,T and V. We use it to give direct proofs of two previously known…
Rigidity for von Neumann algebras given by locally compact groups and their crossed products
Arnaud Brothier, Tobe Deprez, Stefaan Vaes
We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitra…
Crossed-products by locally compact groups: Intermediate subfactors
Rémi Boutonnet, Arnaud Brothier
We study actions of locally compact groups on von Neumann factors and the associated crossed-product von Neumann algebras. In the setting of totally disconnected groups we provide…
On fixed point planar algebras
Arnaud Brothier
To a weighted graph can be associated a bipartite graph planar algebra P. We construct and study the symmetric enveloping inclusion of P. We show that this construction is equivari…