Differential forms with coefficients in 2 2-matrices

Let be a domain in Cm with the canonical complex coordinates z = (z

( ) the set of all (0; k)-forms on of class Cp, and by G

( ) the set of all (s; 0)-forms of the same class; and set G p

( ). Natural operations of addition and

of multiplication by complex scalars turn each of them into a complex linear space. Moreover, we shall consider G

( ) as an algebra with respect to the exterior multiplication “^”; thus, G

( ) is a complex algebra which is associative, distributive, non-commutative, with zero-divisors and with identity. The same is true for G

( ).