Abstract
As we pointed out in 6.2, there are exactly two simple real Lie algebras of dimension 3. These are: the algebra \( {{\mathfrak{g}}_{1}} = \mathfrak{s}\mathfrak{l}\left( {2,R} \right) \) of real matrices of the second order with zero trace and the algebra \( {{\mathfrak{g}}_{2}} = \mathfrak{s}\mathfrak{o} = \left( {3,R} \right) \) of real skew-symmetric matrices of the third order.
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© 1976 Springer-Verlag Berlin Heidelberg
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Kirillov, A.A. (1976). Lie Groups and Lie Algebras. In: Elements of the Theory of Representations. Grundlehren der mathematischen Wissenschaften, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66243-0_18
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DOI: https://doi.org/10.1007/978-3-642-66243-0_18
Publisher Name: Springer, Berlin, Heidelberg
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