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Example 1:
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We first construct two LAVF objects
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Both LAVFs are Lie algebras and L is indeed a subalgebra of LE2
2-dim translation group is subspace of 2-dim Euclidean group
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The centraliser of translations in E(2) is the translations themselves...
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Normaliser of translations in E(2) is E(2)
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Normaliser of E(2) in 'Lie algebra' of all vector fields is 4-dim, and includes E(2) as well as the uniform scalings...
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Example 2:
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L is an affine group on the line (i.e. acts on x only)...
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Normaliser of L in Lie algebra of all vector fields is an infinite Lie pseudogroup
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