Invariant measures on the transversal hull of cone semigroups and some applications

2025/07/09 by Ojito, Danilo Polo, Prodan, Emil, Stoiber, Tom
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2507.06757

Abstract

Let \LL_{\bf v}⊂ \Z^D be a suitable cone semigroup and \A_{\bf v} its reduced semigroup C^*-algebra. In this paper, we compute the \LL_{\bf v}-invariant measures in the transversal hull of the semigroup \LL_{\bf v} that exhibit regularity in the boundaries of \LL_{\bf v}. These measures enable the construction of a trace per-unit hypersurface for observables in \A_{\bf v} supported near the boundaries of \LL_{\bf v}, leading to the construction of appropriate Chern cocycles in the "boundary" ideals of \A_{\bf v}. Our approach applies to both finitely and non-finitely generated cone semigroups. Applications for the bulk-defect correspondence of lattice models of topological insulators are also provided.

Citations

• A space-adiabatic approach for bulk-defect correspondences in lattice models of topological insulators
• On the K-theory of magnetic algebras: Iwatsuka case
• Sharp density discrepancy for cut and project sets: An approach via lattice point counting
• Interface currents and corner states in magnetic quarter-plane systems
• Hyperuniformity and non-hyperuniformity of quasicrystals
• Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems
• Semigroup C*-algebras
• On the K-theory of crossed products by automorphic semigroup actions
• From endomorphisms to automorphisms and back: dilations and full corners

Related

• The cone of lower semicontinuous traces on a C*-algebra
• E-semigroups over closed convex cones
• Boundary quotients of C*-algebras of right LCM semigroups
• Fixed-points in the cone of traces on a C*-algebra
• Operator algebras and representations from commuting semigroup actions