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## Main Question or Discussion Point

Are there cases where there's more than one binary operation to choose from by which to define a Lie algebra for a given vector space?

- Thread starter Rasalhague
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Are there cases where there's more than one binary operation to choose from by which to define a Lie algebra for a given vector space?

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"The [sic] Lie algebra of the vector space R

"The three-dimensional Euclidean space R

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Fredrik

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If you're looking for an example of a vector space with two non-trivial Lie brackets that give us non-isomorphic Lie algbras, I don't have one, but I would be surprised if no such example exists. (By "non-trivial", I mean that it's

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Thanks. That's exactly what I wanted to know.

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