Representations of Yang-Mills algebras

Estanislao Herscovich (1) , Andrea Solotar (2)

1 IF - Institut Fourier
2 Departamento de Matemática [Buenos Aires]

The aim of this article is to describe families of representations of the Yang-Mills algebras YM(n) (n is an element of 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 seperate points of the algebra. In order to prove this result, we prove and use that all Weyl algebras A(r)(k) are epimorphic images of YM(n).

Domaines: Théorie des représentations [math.RT]

Estanislao Herscovich, Andrea Solotar. Representations of Yang-Mills algebras. Annals of Mathematics, 2011, 173 (2), pp.1043-1080. ⟨10.4007/annals.2011.173.2.12⟩. ⟨hal-02009493⟩