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arXiv · 1104.3541

Bianchi spaces and their 3-dimensional isometries as S-expansions of 2-dimensional isometries

Ricardo Caroca·Igor Kondrashuk·Nelson Merino·Felip Nadal
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Abstract

In this paper we show that some 3-dimensional isometry algebras, specifically those of type I, II, III and V (according Bianchi's classification), can be obtained as expansions of the isometries in 2 dimensions. It is shown that in general more than one semigroup will lead to the same result. It is impossible to obtain the algebras of type IV, VI-IX as an expansion from the isometry algebras in 2 dimensions. This means that the first set of algebras has properties that can be obtained from isometries in 2 dimensions while the second set has properties that are in some sense intrinsic in 3 dimensions. All the results are checked with computer programs. This procedure can be generalized to higher dimensions, which could be useful for diverse physical applications.

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Ricardo Caroca, Igor Kondrashuk, Nelson Merino, Felip Nadal. 2011-04-18. Bianchi spaces and their 3-dimensional isometries as S-expansions of 2-dimensional isometries. https://doi.org/10.1088/1751-8113/46/22/225201

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