On hypercomplexifying real forms of arbitrary rank

Details On hypercomplexifying real forms of arbitrary rank On hypercomplexifying real forms of arbitrary rank

2002-09-28

arxiv.org/abs/math/0209396v1

Adv. in Appl. Cliff. Alg. vol. 11, no. 2, 256-271 (2001)

Mathematics

Differential Geometry

5 pages

Scientific paper

For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, followed by quaternionic vectors as a special case. All results are shown to reduce to the established method of complexifying vector fields. For simplicity, differential forms are used rather than vector notation.

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