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The holonomy Lie algebras of neutral metrics in dimension four

The Lie algebra isomorphism between su (1,1)× su (1,1) and o(2,2) is used to obtain a list of subalgebras of the latter. The resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the Lie algebra of the holonomy group of a neutral metric in four dimensions. T...

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Bibliographic Details
Published in:Journal of mathematical physics 2001-05, Vol.42 (5), p.2266-2284
Main Authors: Ghanam, Ryad, Thompson, G.
Format: Article
Language:English
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Summary:The Lie algebra isomorphism between su (1,1)× su (1,1) and o(2,2) is used to obtain a list of subalgebras of the latter. The resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the Lie algebra of the holonomy group of a neutral metric in four dimensions. The conclusions, taken in conjunction with previously known results, furnish a classification of such Lie subalgebras of o(2,2), with only one case remaining unresolved.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1362284