Moyal-Nahm equations

Various aspects of the Nahm equations in three and seven dimensions are inv estigated. The residues of the variables at simple poles in the seven-dimen sional case form an algebra. A large class of matrix representations of thi s algebra is constructed. The large N limit of these equations is taken by replacing the commutators by Moyal brackets, and a set of nontrivial soluti ons in a generalized form of Wigner distribution functions is obtained. (C) 1999 American Institute of Physics. [S0022-2488(99)03706-8].