Applications of the double and the dual numbers. The Bianchi models

Authors

DOI:

https://doi.org/10.31349/RevMexFisE.17.146

Keywords:

Double numbers, dual numbers, cosmology, Lie groups.

Abstract

We show that by using complex, double, and dual numbers one can find the invariant one-forms employed in the metrics of the Bianchi cosmological models. The result is equivalent to find, locally, all the Lie groups of dimension three.

References

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{O}. Gr{o}n and S. Hervik, {it Einstein's General Theory of Relativity} (Springer, New York, 2007), chap. 15.

G.F.R. Ellis, R. Maartens and M.A.H. MacCallum, {it Relativistic Cosmology} (Cambridge University Press, Cambridge, 2012), sec. 18.3.

D.H. Sattinger and O.L. Weaver, {it Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics} (Springer-Verlag, New York, 1986), chaps. 7, 8.

G.F. Torres del Castillo, {it Differentiable Manifolds: A Theoretical Physics Approach}, 2nd edn. (Birkh"auser, New York, 2020) (to be published).

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Published

2020-07-01

How to Cite

[1]
G. F. Torres del Castillo, “Applications of the double and the dual numbers. The Bianchi models”, Rev. Mex. Fis. E, vol. 17, no. 2 Jul-Dec, pp. 146–149, Jul. 2020.