NAIMARK'S PROBLEM FOR GRAPH C*-ALGEBRAS AND LEAVITT PATH ALGEBRAS

Speaker(s)

KULUMANI M. RANGASWAMY

Affiliation

University of Colorado, Colorado Springs, USA

Language of the talk

English

Date

Nov. 19, 2025, 5:15 p.m.

Information about the event

IMPAN - Room 405

Title in Polish

NAIMARK'S PROBLEM FOR GRAPH C*-ALGEBRAS AND LEAVITT PATH ALGEBRAS

Seminar

North Atlantic Noncommutative Geometry Seminar

---

Naimark's problem asks whether a C*-algebra having a unique irreducible *-representation up to unitary equivalence is isomorphic to the C*-algebra of compact operators on some (not necessarily separable) Hilbert space. Here, we consider Naimark's problem for graph C*-algebras. First, it is shown how boundary paths in a graph can be used to construct irreducible representations of the associated graph C*-algebras. Such constructions enable us to prove that Naimark's problem has a positive answer for graph C*-algebras. Better still, the algebraic analogue of Naimark's problem is shown to have a positive answer for Leavitt path algebras. We also characterize when a graph C*-algebra has a countable (finite or countably infinite) spectrum, and prove that, in this case, the unitary equivalence classes of irreducible representations are in one-to-one correspondence with the shift-tail equivalence classes of boundary paths of the graph. (Joint work with Mark Tomforde.)

---