EXTENDED PATH HOMOMORPHISMS OF DIRECTED GRAPHS

Speaker(s)

GILLES G. DE CASTRO

Affiliation

Universidade Federal de Santa Catarina, Florianópolis, Brazil

Language of the talk

English

Date

May 20, 2026, 5:15 p.m.

Information about the event

ZOOM

Title in Polish

EXTENDED PATH HOMOMORPHISMS OF DIRECTED GRAPHS

Seminar

North Atlantic Noncommutative Geometry Seminar

---

Leavitt path algebras and graph C*-algebras are objects associated with directed graphs. They have deep connections with symbolic dynamics, and the former contains a class of rings that do not satisfy the Invariant Basis Number (IBN) property. Motivated by examples in noncommutative topology, we have been investigating what kind of morphisms can be defined on graphs to make these constructions functorial. The goal is to define these morphisms broadly enough to include examples of interest, but not so general that the combinatorial aspects of the graph are lost. In this talk, I will explain several of these notions and how we can use inverse semigroups to define what we call extended path homomorphisms of directed graphs. Leavitt path algebras are quotients of inverse semigroup algebras, and one of the primary difficulties is identifying the appropriate properties for extended path homomorphisms to handle these quotients. (Based on joint works with F. D’Andrea, P. M. Hajac, M. Lowiel, R. Meyer, and E. A. Pacheco.)

---