finsler geometry, hypercomplex numbers and physics
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Three-numbers, which cube of norm is nondegenerate three-form
2004jap | Garas`ko G. I.

Arbitrary three-form can be put in a canonical form. The requirement of existence of two-parametric Abelian Lie group to play the role of group of symmetry for three-form admits selecting the three-forms that correspond to three-numbers and finding all the three-numbers which cube of norm is a non-degenerate three-form with respect to a special coordinate system. There are exactly two (up to isomorphism) such sets of hypercomplex numbers, namely the sets: C3, H3. They can be regarded as generalizations of complex and binary (hyperbolic) bi-numbers to the case of three-numbers.


English: Russian:
01-11-e.pdf, 216,896 Kb, PDF 01-11.pdf, 451,575 Kb, PDF
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