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A note on the generalized neutral orthogonal group in dimension four. (English) Zbl 1145.70008
Summary: We study the main properties of generalized neutral orthogonal group \(O(2,2)\) and its Lie algebra \(o(2,2)\) and give an explicit isomorphism between Lie algebras \({\mathfrak{su}}(1,1)\oplus {\mathfrak{su}}(1,1)\) and \(o(2,2)\). We use this isomorphism to classify the subalgebras of \(o(2,2)\).

MSC:
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
22E70 Applications of Lie groups to the sciences; explicit representations
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