EXTENDED COMPLEX NUMBER ANALYSIS AND CONFORMAL-LIKE TRANSFORMATIONS

In a previous paper, we considered a possible extension of complex num bers, as well as its connected trigonometry. We now examine, the prope rties of complex analysis that can be transposed to these numbers: thi s goes from analyticity conditions to the residue theorem. We then sho w that the associated conformal symmetry is infinite and leads to n (n is the dimension of the algebra) copies of the Virasoro algebra, and define, with an appropriate prolongation of the function z --> 1/z, th e analogue of the global conformal group. These algebras could be used for the description of scale invariant systems in more than two dimen sions. We also give a Z(n)-graded product adapted to these numbers. (C ) 1995 Academic Press, Inc.