7 papers
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…
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…
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…
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…