Translation Invariant States on Twisted Algebras on a Lattice

TL;DR

This paper constructs a twisted algebra on a lattice with a shift operation and proves that, under certain conditions, the only translation-invariant state is the tracial state, highlighting unique invariant state properties.

Contribution

It introduces a new algebra with twisted commutation relations and establishes the uniqueness of the translation-invariant state under specific irregularity conditions.

Findings

Tracial state is the unique translation-invariant state.

Construction of algebra with twisted commutation relations.

Proof of invariance properties under shift.

Abstract

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state.