Operator algebras seminar

Speaker: Christopher Linden (University of Illinois at Urbana-Champaign)

Title: Continued fraction and permutative representations of Cuntz algebras.

Abstract: Permutative representations are a tractable class of representations of Cuntz algebras, introduced and classified by Bratteli and Jorgensen. Recent work on "slow" continued fraction algorithms can be applied to label unitary equivalence classes of irreducible permutative representations by orbits of a group action. This generalizes a result of Hayashi, Kawamura, and Lascu. Combinatorial relationships between different slow continued fraction algorithms can be understood in terms of monomial embeddings of Cuntz algebras. If time permits, I will also discuss how these embeddings are useful in the construction of self-adjoint free semigroupoid algebras.