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VII. References

Baker, H. F. (1901): On the Exponential Theorem for a Simply Transitive Continuous Group…, Proceedings of the London Mathematical Society, Vol. 34, pp. 91 – 127

This work is the only one we know of mentioning explicitly this simply transitive group as a possible group of space transformations. It is with respect to this group that the roots of a cubic form a vector, which also happens to be a real space vector for which we can use a regular geometrical decomposition on the octahedral plane. As a group vector, for its description we have to use the coordinate basis, for the basis given by the infinitesimal generators is not commutative (as a matter of fact it is one of the group generators). The importance of these transformations from physical point of view will be discussed elsewhere. Otherwise, the above work is important in itself as a historical reference: it is one of the works that contributed to the well known Baker-Campbell-Hausdorff-… types of formulas, so often used in contemporary Physics, mostly after the developments in Quantum Optics that took place in the decades 1960 – 1980.

Barbilian, D. (1938): Riemannsche Raum Cubischer Binärformen, Comptes Rendus de l’Academie Roumaine des Sciences, Vol. 2, p. 345

Burnside, W. S., Panton, A. W. (1960): The Theory of Equations, Dover Publications

Cocolicchio, D., Viggiano, M. (2000): The Diagonalization of Cubic Matrices, Journal of Physics A: Mathematical and General, Vol. 33, pp. 5669 – 5673

Fels, M., Olver, P. J. (1998): Moving Coframes I, Acta Applicandae Mathematicae, Vol. 51, pp. 161 – 213;

Flanders, H. (1989): Differential Forms with Applications to the Physical Sciences, Dover Publications, New York

Nickalls, R. W. D. (1993): A New Approach To Solving The Cubic: Cardan’s Solution Revealed, The Mathematical Gazette, Vol. 77, pp. 354 – 359

Novozhilov, V. V. (1951): The Relation Between Stress and Strain in a Non-Linearly Elastic Medium, Prikladnaya Matematika i Mekhanika, Vol. 15, pp. 183 – 194

Sasaki, R. (1979): Soliton Equations and Pseudospherical Surfaces, Nuclear Physics Vol. B154, pp. 343 – 357

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