Leo algknt: Created page with "'''Lie algebra of dimensions 1 and 2''' 1. '''one-dimensional Lie algebras''' are unique up to isomorphism. For if $\mathfrak{g} = \langle x \rangle$ is a one d..."

2018-07-04T06:27:24Z

Created page with "'''Lie algebra of dimensions 1 and 2''' 1. '''one-dimensional Lie algebras''' are unique up to isomorphism. For if <math>\mathfrak{g} = \langle x \rangle </math> is a one d..."

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'''Lie algebra of dimensions 1 and 2'''

1. '''one-dimensional Lie algebras''' are unique up to isomorphism. For if <math>\mathfrak{g} = \langle x \rangle </math> is a one dimensional Lie algebra, then since the bracket is antisymmetric, we have <math>[x, x] = 0</math>. Thus the bracket is zero and <math>\mathfrak{g}</math> is unique up to isomorphism.

2. <math>\mathfrak{g} = \mathbb{F}^2 = \{ax + by \;|\; a, b \in \mathbb{F}\}</math>. <math>\mathfrak{g}</math> 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 <math>[x, y] = x</math>.

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Leo algknt: Created page with "'''Lie algebra of dimensions 1 and 2''' 1. '''one-dimensional Lie algebras''' are unique up to isomorphism. For if \mathfrak{g} = \langle x \rangle is a one d..."

Leo algknt: Created page with "'''Lie algebra of dimensions 1 and 2''' 1. '''one-dimensional Lie algebras''' are unique up to isomorphism. For if $\mathfrak{g} = \langle x \rangle$ is a one d..."