n-Dimensional dual complex numbers.

It is well-known that the quadratic algebras Q _a,b = { z| z = x + qy, q ² = a + qb , a, b, x, y ε ℝ, q ∉ ℝ }, also expressible as ℝ[ x]/( x ² - bx - a), are, up to isomorphism, equivalent to just three algebras, corresponding to elliptic, parabolic and hyperbolic. These three types are usually represented by Q _−1,0, Q _0,0, Q _1,0 and called complex numbers, dual complex numbers and hyperbolic complex numbers, respectively. Each in turn describes a Euclidian, Galilean and Minkowskian plane. The hyperbolic complex numbers thus provide a 2-dimensional spacetime for special relativity physics (see e.g. [6]) and the dual complex numbers a 2-dimensional spacetime for Newtonian physics (see e.g. [17]). The present authors considered extensions of the hyperbolic complex numbers to n dimensions in [8], and here, in somewhat parallel fashion, some elements of algebra (in Section 1) and analysis (in Section 2) will be presented for n-dimensional dual complex numbers. [ABSTRACT FROM AUTHOR]