Classification in Dimension Less Than 3
- Dimension 0: The only Lie algebra is the abelian Lie algebra R0.
- Dimension 1: The only Lie algebra is the abelian Lie algebra R1, with outer automorphism group the group of non-zero real numbers.
- Dimension 2: There are two Lie algebras:
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- (1) The abelian Lie algebra R2, with outer automorphism group GL2(R).
- (2) The solvable Lie algebra of 2×2 upper triangular matrices of trace 0. The simply connected group has trivial center and outer automorphism group of order 2.
Read more about this topic: Bianchi Classification
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