Relative ultragraph algebras and infinite interval maps

2025/08/27 by Eidt, Ben-Hur, Gonçalves, Daniel, Royer, Danilo
#37E05 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 37E10

paper · doi:10.48550/arxiv.2508.19835

Abstract

In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely connected to, and indeed motivated by, the dynamics of certain interval maps that we call infinite Markov maps. The central point is that these algebras provide the natural framework in which representations induced by such maps are defined.

Citations

• Unifying interval maps and branching systems with applications to relative graph C*-algebras
• Representations of relative Cohn path algebras
• Branching Systems for Higher-Rank Graph C*-algebras
• Branching Systems and General Cuntz-Krieger Uniqueness Theorem for\n Ultragraph C*-algebras
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• Unitary equivalence of representations of graph algebras and branching systems
• Graph C*-algebras, branching systems and the Perron-Frobenius operator
• Cuntz-Krieger algebras and wavelets on fractals
• Ultragraph C*-algebras via topological quivers
• Wavelet constructions in non-linear dynamics
• Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs
• Adding tails to C*-correspondences
• Recursive Fermion System in Cuntz Algebra.I -- Embeddings of Fermion Algebra into Cuntz Algebra ---
• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs
• Simplicity of ultragraph algebras

Related

• Unifying interval maps and branching systems with applications to relative graph C*-algebras
• Representations and the reduction theorem for ultragraph Leavitt path algebras
• On graph algebras from interval maps
• Branching Systems and General Cuntz-Krieger Uniqueness Theorem for\n Ultragraph C*-algebras
• Simplicity of ultragraph algebras