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

Prelegent(ci)

KULUMANI M. RANGASWAMY

Afiliacja

University of Colorado, Colorado Springs, USA

Język referatu

angielski

Termin

19 listopada 2025 17:15

Informacje na temat wydarzenia

IMPAN - Room 405 & zoom

Tytuł w języku polskim

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

Seminarium

North Atlantic Noncommutative Geometry Seminar

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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.)

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