17 citations · 162 across the 31 of their papers we have counts for
31 papers
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…
Piecewise Linear Equivariant Maps for Compact Groups
Valeriano Aiello
Motivated by equivariant neural networks, we study piecewise linear equivariant maps between finite-dimensional real representations of compact groups. We show that all genuinely n…
On the Ryll-Nardzewski Theorem for Quantum Stochastic Processes
Valeriano Aiello, Simone Del Vecchio, Stefano Rossi
We prove a Ryll-Nardzewski Theorem for quantum stochastic processes, that shows that under natural assumptions which generalize the classical probability setting, the distributiona…
The Motzkin subproduct system
Valeriano Aiello, Simone Del Vecchio, Stefano Rossi
We introduce a subproduct system of finite-dimensional Hilbert spaces by using the Motzkin planar algebra and its Motzkin Jones-Wenzl idempotents, which generalizes the Temperley-L…
An extension of Krishnan's central limit theorem to the Brown-Thompson groups
Valeriano Aiello
We extend a central limit theorem, recently established for the Thompson group by Krishnan, to the Brown-Thompson groups , where is any integer greater than or equ…
A computational study of the number of connected components of positive Thompson links
Valeriano Aiello, Stefano Iovieno
Almost a decade ago Vaughan Jones introduced a method to produce knots from elements of the Thompson groups , which was later extended to the Brown-Thompson group . In this…
The planar -colorable subgroup of Thompson's group and its even part
Valeriano Aiello, Tatiana Nagnibeda
We study the planar -colorable subgroup of Thompson's group and its even part . The latter is obtained by cutting with a…
An introduction to Thompson knot theory and to Jones subgroups
Valeriano Aiello
We review a constructions of knots from elements of the Thompson groups due to Vaughan Jones, which comes in two flavours: oriented and unoriented.
On the Jones polynomial modulo primes
Valeriano Aiello, Sebastian Baader, Livio Ferretti
We derive an upper bound on the density of Jones polynomials of knots modulo a prime number , within a sufficiently large degree range: . As an application, we classify k…
On the cyclic automorphism of the Cuntz algebra and its fixed-point algebra
Valeriano Aiello, Stefano Rossi
We investigate the structure of the fixed-point algebra of under the action of the cyclic permutation of the generating isometries. We prove that it is -isomorph…
Arborescence of positive Thompson links
Valeriano Aiello, Sebastian Baader
We show that the links associated with positive elements of the Thompson group coincide with the closures of bipartite arborescent tangles.
On the -colorable subgroup and maximal subgroups of Thompson's group
Valeriano Aiello, Tatiana Nagnibeda
In his work on representations of Thompson's group , Vaughan Jones defined and studied the -\emph{colorable subgroup} of . Later, Ren showed that it is isomo…
Spectral triples on irreversible -dynamical systems
Valeriano Aiello, Daniele Guido, Tommaso Isola
Given a spectral triple on a -algebra together with a unital injective endomorphism , the problem of defining a suitable crossed product -algebra endowed…
On the entropy and index of the winding endomorphisms of p-adic ring C-algebras
Valeriano Aiello, Stefano Rossi
For , the -adic ring -algebra is the universal -algebra generated by a unitary and an isometry such that and $\sum_{l=…
Positive oriented Thompson links
Valeriano Aiello, Sebastian Baader
We prove that the links associated with positive elements of the oriented subgroup of the Thompson group are positive.
A Spectral Triple for a Solenoid Based on the Sierpinski Gasket
Valeriano Aiello, Daniele Guido, Tommaso Isola
The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical fea…
On the oriented Thompson subgroup and its relatives in higher Brown-Thompson groups
Valeriano Aiello, Tatiana Nagnibeda
A few years ago the so-called oriented subgroup of the Thompson group was introduced by V. Jones while investigating the connections between subfactors and conformal f…
A Fejér theorem for boundary quotients arising from algebraic dynamical systems
Valeriano Aiello, Roberto Conti, Stefano Rossi
A Fejér-type theorem is proved within the framework of -algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a resul…
Remarks on some maximal subgroups of and on the -index of knots
Valeriano Aiello
We demonstrate that three maximal subgroups of infinite index in the rectangular subgroup \( K_{(2,2)} \) of the Thompson group \( F \), each containing Jones's \( 3 \)-colorable s…
On spectral measures for certain unitary representations of R. Thompson's group F
Valeriano Aiello, Vaughan F. R. Jones
The Hilbert space of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group via local scale transformations…
Normalizers and permutative endomorphisms of the -adic ring -algebra
Valeriano Aiello, Roberto Conti, Stefano Rossi
A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra in the -adic ring -algebra , which generalize…
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…
On the Alexander Theorem for the oriented Thompson group
Valeriano Aiello
In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group . In this paper we prove, b…
Permutative representations of the -adic ring -algebra
Valeriano Aiello, Roberto Conti, Stefano Rossi
The notion of permutative representation is generalized to the -adic ring -algebra . Permutative representations of are then investigated w…