Representation theory of Yang-Mills algebras

Abstract

The aim of this article is to describe families of representations of the Yang-Mills algebras YM(n) (n∈N≥2) defined by A. Connes and M. Dubois-Violette. We first describe some irreducible finite dimensional representations. Next, we provide families of infinite dimensional representations of YM, big enough to separate points of the algebra. In order to prove this result, we prove and use that all Weyl algebras Ar(k) are epimorphic images of YM(n).