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Dualizability and graph algebras. (English) Zbl 0945.08001

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.

MSC:

08A05 Structure theory of algebraic structures
05C99 Graph theory
08C15 Quasivarieties
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
03C05 Equational classes, universal algebra in model theory
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