  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 a
paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally
supersymmetric Yang-Mills theories. In this paper we collected those of our
results which are correct without assumption of supersymmetry and used them to
give rigorous proofs of some results of the cited paper. We consider two
different algebraic interpretations of Yang-Mills theory - in terms of
A_{\infty}-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 algebras in question.
