PARAGRASSMANN DIFFERENTIAL-CALCULUS

This paper significantly extends and generalizes the paragrassmann cal culus of our previous paper [1]. Here we discuss explicit general cons tructions for paragrassmann calculus with one and many variables. For one variable, nondegenerate differentiation algebras are identified an d shown to be equivalent to the algebra of (p + 1) x (p + 1) complex m atrices. If (p + 1) is a prime integer, the algebra is nondegenerate a nd so unique. We then give a general construction of many-variable dif ferentiation algebras. Some particular examples are related to multi-p arametric quantum deformations of the harmonic oscillators.