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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
Keywords:
classification; explicit isomorphism