GENERALIZATION OF THE ALGEBRA OF THE MATRIX PSEUDODIFFERENTIAL-OPERATORS

We introduce the new nonhomogeneous graded matrix algebra Mat(n)(R) ov er the ring R of the pseudodifferential operators of the arbitrary ord ers. This algebra forms the generalization of the algebra of the stand ard matrix pseudodifferential operators. We show that the Mat(n)(R) al gebra admits the nontrivial central extension. The case n = 2 is consi dered in some detail. As the example we consider the Mat(2)(W1+infinit y), Mat(2)(Virasoro) and Mat(2)(sl(2,C)) algebras. (C) 1998 American I nstitute of Physics. [S0022-2488(97)03111-3].