Multicomplex number
Appearance
In mathematics, the multicomplex numbers, , form a commutative n dimensional algebra generated by one element e which satisfies . A multicomplex number x can be written as
with and real. Two equivalent possible matrix representations of the algebra can be generated by choosing
where q is an ordinary complex nth root of -1, i.e. q = exp(-iπ/n).
It is possible to write any multicomplex number x (with ) in an exponential representation
- .
A special case of multicomplex numbers are the bicomplex numbers with n=2, which are isomorphic to C⊗C.
References
- G. Baley Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker Inc., New York, 1991
- Michel Rausch de Traubenberg, Algèbres de Clifford, Supersymétrie et Symétries Zn: Applications en Théorie des Champs, Habilitation, Université Louis Pasteur, Strasbourg 1997 pp. 20-29 (in French).