Graph Douglas 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.

Higher Rank Graph Algebras

These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.

Dualizability and graph algebras

We characterize the finite graph algebras which are dualizable. Indeed, a finite graph algebra is dualizable if and only if each connected component of the underlying graph is either complete or bipartite complete (or a single point).

Corners of Graph Algebras

It is known that given a directed graph E and a subset X of vertices, the sum Σ v∈X P v of vertex projections in the C *-algebra of E converges strictly in the multiplier algebra to a projection P X. Here we give a construction which, in certain cases, produces a directed graph F such that C * (F) is isomorphic to the corner P X C * (E)P X. Corners of this type arise naturally as the fixed poin...

Graph of BCI-Algebras