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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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Published in: | Journal of mathematical physics 2001-05, Vol.42 (5), p.2266-2284 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0022-2488 1089-7658 |
DOI: | 10.1063/1.1362284 |