Finite Bases for Flat Graph Algebras

Full Duality among Graph Algebras and Flat Graph Algebras

We prove that among finite graph algebras and among finite flat graph algebras, dualizability, full dualizability, strong dualizability and entropicity are all equivalent. Any finite (flat) graph algebra which is not dualizable must be inherently non-κ-dualizable for every infinite cardinal κ. A new, general method for proving strong duality is presented.

Finite Dimensional Point Derivations for Graph Algebras

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze t...

The Membership Problem in Finite Flat Hypergraph Algebras

Residual Finiteness and Finite Equational Bases: Undecidable Properties of Finite Algebras

Flat Dimension Growth for C-algebras

Simple and nuclear C-algebras which fail to absorb the Jiang-Su algebra tensorially have settled many open questions in the theory of nuclear C-algebras, but have been little studied in their own right. This is due partly to a dearth of invariants sensitive to differences between such algebras. We present two new real-valued invariants to fill this void: the dimension-rank ratio (for unital AH ...