  We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM
theory) and its dimensional reductions, in particular, BFSS and IKKT models. We
formulate these theories using algebraic techniques based on application of
differential graded Lie algebras and associative algebras as well as of more
general objects, L_{\infty}- and A_{\infty}- algebras.
  We show that using pure spinor formulation of 10D SUSY YM theory equations of
motion and isotwistor formalism one can interpret these equations as
Maurer-Cartan equations for some differential Lie algebra. This statement can
be used to write BV action functional of 10D SUSY YM theory in Chern-Simons
form. The differential Lie algebra we constructed is closely related to
differential associative algebra Omega of (0, k)-forms on some supermanifold;
the Lie algebra is tensor product of Omega and matrix algebra .
  We construct several other algebras that are quasiisomorphic to Omega and,
therefore, also can be used to give BV formulation of 10D SUSY YM theory and
its reductions. In particular, Omega is quasiisomorphic to the algebra B
constructed by Berkovits. The algebras Omega_0 and B_0 obtained from Omega and
B by means of reduction to a point can be used to give a BV-formulation of IKKT
model.
  We introduce associative algebra SYM as algebra where relations are defined
as equations of motion of IKKT model and show that Koszul dual to the algebra
B_0 is quasiisomorphic to SYM.
