GRADED LOCALLY FINITE AND GRADED JUST INFINITE STEINBERG ALGEBRAS

Speaker(s)

DANIEL VAN WYK

Affiliation

Fairfield University, Connecticut, USA

Language of the talk

English

Date

May 13, 2026, 5:15 p.m.

Information about the event

IMPAN - Room 405 & zoom

Title in Polish

GRADED LOCALLY FINITE AND GRADED JUST INFINITE STEINBERG ALGEBRAS

Seminar

North Atlantic Noncommutative Geometry Seminar

---

We will begin the talk by briefly reviewing the characterizations of locally finite and just infinite Leavitt path algebras, found by Abrams, Pino, and Molina. They consider Leavitt path algebras with the canonical Z-grading. After the brief review, I will discuss recent efforts to extend their results to ample groupoid algebras, also known as Steinberg algebras, with an arbitrary grading induced by a continuous cocycle into a discrete group. We will present a full characterization of graded locally finite Steinberg algebras, and a partial characterization of just infinite Steinberg algebras. If we specialize to the case where the unit fibre is strongly effective, we obtain a full characterization of graded just infinite Steinberg algebras. We will present various results, including that, for locally finite Steinberg algebras, being graded just infinite is equivalent to being graded simple. Finally, we will discuss Deaconu-Renault groupoids and groupoids associated with subshifts as applications.

---