Classifying higher rank analytic Toeplitz algebras
نویسنده
چکیده
To a higher rank directed graph (Λ, d), in the sense of Kumjian and Pask, 2000, one can associate natural noncommutative analytic Toeplitz algebras, both weakly closed and norm closed. We introduce methods for the classification of these algebras in the case of single vertex graphs.
منابع مشابه
Higher-rank Graph C∗-algebras: an Inverse Semigroup and Groupoid Approach
We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.
متن کاملProduct Systems of Graphs and the Toeplitz Algebras of Higher-rank Graphs
Abstract. There has recently been much interest in the C∗-algebras of directed graphs. Here we consider product systems E of directed graphs over semigroups and associated C∗-algebras C∗(E) and T C∗(E) which generalise the higher-rank graph algebras of Kumjian-Pask and their Toeplitz analogues. We study these algebras by constructing from E a product system X(E) of Hilbert bimodules, and applyi...
متن کاملMultiply generated dynamical systems and the duality of higher rank graph algebras
We define a semidirect product groupoid of a system of partially defined local homeomorphisms T = (T1, . . . , Tr). We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use this construction for higher rank graph algebras in order to give a topological interpretation for the duality in E-theory between C∗(Λ) and C∗(Λop). Introducti...
متن کاملToeplitz Operators and Solvable C*-algebras on Hermitian Symmetric Spaces
Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...
متن کاملWhich subnormal Toeplitz operators are either normal or analytic ?
We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos’s Problem 5: Which subnormal block Toeplitz operators are either normal or analytic ? We extend and prove Abrahamse’s Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007