Algebraic structure of Yang-Mills theory

In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with [15] and devoted to maximally supersymmetric Yang-Mills theories. In this paper we collect those of our results which hold without the assumption of supersymmetry and use them to give rigorous proofs of some results of [15]. We consider two different algebraic interpretations of Yang-Mills theory—in terms of A _∞-algebras and in terms of representations of Lie algebras (or associative algebras). We analyze the relations between these two approaches and calculate some Hochschild (co)homology of the algebras in question.