Dualizability and graph algebras (Q1972139)

This paper serves two purposes: it provides a characterization of finite graph algebras which are dualizable, and it elaborates some techniques which promise to be useful in establishing that various finite algebras are not dualizable. Those techniques are also applied herein to sharpen some existing nondualizability results. The main result of this paper is the equivalence: A finite graph algebra is dualizable iff each connected component of the underlying graph is either complete or complete bipartite (or a single point). This in turn is known to be equivalent to the graph algebra having a finitely axiomatizable equational theory.