Directed graphs, variations on directed graphs, and their $C^*$-algebras
Volume 130 / 2026
Banach Center Publications 130 (2026), 59-73
MSC: Primary 46L80; Secondary 20L05
DOI: 10.4064/bc130-3
Abstract
We describe some current developments in the use of combinatorial objects to define $C^*$-algebras from a historical point of view. Beginning with the origins of graph $C^*$-algebras, we motivate the definitions for submonoids of groups, and for left cancellative small categories generally, giving the precise construction for the finitely aligned case. We close with a family of interesting examples based on this construction.
