This is a joint work with Estanislao Herscovich.

Yang-Mills algebras have been defined by Alain Connes and Michel Dubois-Violette in connection to some problems arising from string theory and noncommutative quantum field theory.

Although it is possible to describe in a simple way every irreducible finite dimensional representation, the task of characterizing the complete category of representations of a Yang-Mills algebra is rather difficult.

The aim of this talk is threefold.

In the first place, I will recall the general definitions and the main properties of these algebras.

Then, I will focus on exhibiting certain families of representations fine enough to separate elements of the Yang-Mills algebras.

Finally, I shall also present several computations in relation to homological properties for these algebras, in particular, the Hochschild and Cyclic homology.