Natural dualities, such as Stone duality, are useful because they allow one to translate algebraic questions into the potentially simpler and usually more intuitive setting of a topological structure. If these dualities exist for particular classes of algebras, then they can be obtained in a systematic way from particular generating algebras and corresponding topological structures. A generating algebra is dualizable if it allows for such a duality. Dualizability of an algebra however is a mysterious property, and the deviding line between dualizing algebras and nondualizing ones is only understood in a few wellbehaved classes of algebras. We have recently shown that a particular property, namely supernilpotence, is strong enough to force an algebra to be nondualizable. In the talk, we will give an introduction to dualizability, present our results, and demonstrate some of the methods used in our proofs. This is joint work with Peter Mayr (JKU Linz).
