5 papers
The prime spectrum of the talented monoid of a higher-rank graph and applications
Roozbeh Hazrat, Promit Mukherjee
In this paper, we further investigate the role of the graded Grothendieck group $K_0^{\gr}$ and its positive cone (the talented monoid) as an effective tool for distinguishing stru…
Some more talents of the talented monoid of a higher-rank graph
Roozbeh Hazrat, Huanhuan Li, Promit Mukherjee
In this paper, we explore the idea that the graded Grothendieck group , or equivalently its positive cone, the talented monoid, can detect the structural type of higher-r…
Higher-Dimensional Symbolic Dynamics: A Textile Framework For 3-graphs
Roozbeh Hazrat, Promit Mukherjee, Sujit Kumar Sardar
Textile systems are best known to model two-dimensional shifts of finite type. In this article, we associate a discrete algebra with a textile system and provide a groupoid model f…
Higher-rank graphs and the graded -theory of Kumjian-Pask algebras
Roozbeh Hazrat, Promit Mukherjee, David Pask +1
This paper lays out the foundations of graded -theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potentia…
The Talented Monoid of Higher-Rank Graphs with Applications to Kumjian-Pask Algebras
Roozbeh Hazrat, Promit Mukherjee, David Pask +1
Given a row-finite higher-rank -graph , we define a commutative monoid which is a higher-rank analogue of the talented monoid of a directed graph. The talented monoid $…