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Some more talents of the talented monoid of a higher-rank graph · arXivDesk

2608.12798Aug 13, 2026

Some more talents of the talented monoid of a higher-rank graph

Roozbeh Hazrat, Huanhuan Li, Promit Mukherjee

Abstract

In this paper, we explore the idea that the graded Grothendieck group $K_0^{gr}$ , or equivalently its positive cone, the talented monoid, can detect the structural type of higher-rank graph algebras (i.e., higher-rank graph $C^*$ -algebras and Kumjian--Pask algebras). We show that the talented monoid captures some of the essential geometric information of a higher-rank graph, including the existence of cycles with and without entrances. In turn, we show that the graded $K$

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In this paper, we explore the idea that the graded Grothendieck group K₀^gr, or equivalently its positive cone, the talented monoid, can detect the structural type of higher-rank graph algebras (i.e., higher-rank graph C^*-algebras and Kumjian--Pask algebras). We show that the talented monoid captures some of the essential geometric information of a higher-rank graph, including the existence of cycles with and without entrances.

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In this paper, we explore the idea that the graded Grothendieck group K₀^gr, or equivalently its positive cone, the talented monoid, can detect the structural type of higher-rank graph algebras (i.e., higher-rank graph C^*-algebras and Kumjian--Pask algebras).