arXiv subjects

Roberto Conti

Publications and source records attributed to Roberto Conti.

62 records · Page 4Linked to original sources

arXiv2008

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.

math.OA↗

arXiv2007

Extension of automorphisms to C*-crossed products with non-trivial centre

Given a quasi-special endomorphism $ρ$ of a C*-algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by $ρ$. Exploiting some aspects of the underlying generalized Doplicher-Roberts duality theory based on Pimsner algebras, an obstruction to the existence of such extensions is found and described in terms of sections of a suitable group bundle.

math.OA↗

arXiv2005

A Category of Spectral Triples and Discrete Groups with Length Function

In the context of A. Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. A. Connes' construction of spectral triples for group algebras is a covariant functor from the category of discrete groups with length functions to that of spectral triples. Several interesting lines for future study of the categorical properties of spectral triples and their variants are suggested.

math.OA↗

arXiv2003

Classification of subsystems for graded-local nets with trivial superselection structure

We classify Haag-dual Poincaré covariant subsystems $\B\subset \F$ of a graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net $\F_\A$ of a net $\A$ of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial internal symmetries, such an observable net $\A$ is generated by (the abstract versions of) the local energy-momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum Noether theorem. Moreover, for a net $\A$ of local observables as above, we also classify the Poincaré covariant local extensions $\B \supset \A$ which preserve the dynamics.

math.OA↗

arXiv2002

On infinite tensor products of projective unitary representations

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with CCR-representations of bilinear maps. Detailed computations are presented in the case where G is a finitely generated free abelian group. We also discuss an extension problem about product type actions of G, where the projective representation theory of G plays a central role.

math.OA↗

arXiv2000

Classification of Subsystems for Local Nets with Trivial Superselection Structure

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is the fixed point net under a compact group action on one component in a suitable tensor product decomposition of F. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors.

math.OA↗

arXiv2000

Superselection Theory for Subsystems

An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed-point net of the field net under a compact group. This compact group is its canonical gauge group if the occurrence of sectors with infinite statistics can be ruled out for the observable net and its vacuum Hilbert space is separable.

math.OA↗

arXiv1997

Covariant Sectors with Infinite Dimension and Positivity of the Energy

We consider a Moebius covariant sector, possibly with infinite dimension, of a local conformal net of von Neumann algebras on the circle. If the sector has finite index, it has automatically positive energy. In the infinite index case, we show the spectrum of the energy always to contain the positive real line, but, as seen by an example, it may contain negative values. We then consider nets with Haag duality on the real line, or equivalently sectors with non-solitonic extension to the dual net; we give a criterion for irreducible sectors to have positive energy, namely this is the case iff there exists an unbounded Moebius covariant left inverse. As a consequence the class of sectors with positive energy is stable under composition, conjugation and direct integral decomposition.

funct-an↗