# A Finite Dimensional Introduction to Operator Algebra

@inproceedings{Muhly1997AFD, title={A Finite Dimensional Introduction to Operator Algebra}, author={Paul S. Muhly}, year={1997} }

This article surveys some recent advances in operator algebra that were inspired by considerations from ring theory, particularly the representation theory of finite dimensional algebras.

## 42 Citations

Canonical Models for Representations of Hardy Algebras

- Mathematics
- 2004

Abstract.We develop a model theory for completely non coisometric representations of the Hardy algebra of a W*-correspondence defined over a von Neumann algebra. It follows very closely the model…

A Halmos Doctrine and Shifts on Hilbert Space

- Mathematics
- 2010

This a survey of some recent work on noncommutative function theory related to tensor algebras that derives in part from Paul Halmos’s paper, Shifts on Hilbert space.

Nest Representations of Directed Graph Algebras

- Mathematics
- 2004

This paper is a comprehensive study of the nest representations for the free semigroupoid algebra LG of a countable directed graph G as well as its norm‐closed counterpart, the tensor algebra T+(G).

Universal operator algebras of directed graphs

- Mathematics
- 2004

We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits.…

On quotients of tensor algebras and their C*-envelopes

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2000

Abstract We identify the C*-envelopes of certain quotients of tensor algebras over C*-correspondences.

Notes on C*-algebras of graphs

- Mathematics
- 2003

C*-algebras of graphs include up to strong Morita equivalence all af algebras, Cuntz-Krieger algebras and the Toeplitz algebra. Our survey discusses recent developments and related constructions.

Partly Free Algebras From Directed Graphs

- Mathematics
- 2004

We say that a nonselfadjoint operator algebra is partly free if it contains a free semigroup algebra. Motivation for such algebras occurs in the setting of what we call free semigroupoid algebras.…

Progress in noncommutative function theory

- Mathematics
- 2011

In this expository paper, we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator…

Progress in noncommutative function theory

- Mathematics
- 2010

In this expository paper, we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator…

Cohomology of Hopf C*‐Algebras and Hopf Von Neumann Algebras

- Mathematics
- 2001

We define two canonical cohomology theories for Hopf C*‐algebras and for Hopf von Neumann algebras (with coefficients in their comodules). We then study the situations when these cohomologies vanish.…

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