Generalization of the algebra of the matrix pseudodifferential operators

Abstract

We introduce the new nonhomogeneous graded matrix algebra Matn(R) over the ring ℜ of the pseudodifferential operators of the arbitrary orders. This algebra forms the generalization of the algebra of the standard matrix pseudodifferential operators. We show that the Matn(R) algebra admits the nontrivial central extension. The case n=2 is considered in some detail. As the example we consider the Mat2(W1+∞), Mat2(Virasoro) and Mat2(sl(2,C)) algebras.