Notes for AKT-140224/0:27:53: Difference between revisions
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Latest revision as of 02:27, 4 July 2018
Lie algebra of dimensions 1 and 2
1. one-dimensional Lie algebras are unique up to isomorphism. For if is a one dimensional Lie algebra, then since the bracket is antisymmetric, we have . Thus the bracket is zero and is unique up to isomorphism.
2. . is a two-dimensional Lie algebra. There are only two of such up to isomorphism, that is, the one with the bracket equal to zero and the other with bracket .