lie algebra

math6

hi friends !!
it is well known that a Lie algebra over K is a K-vector space g equipped
of a K-bilinear, called Lie bracket. I ask how can we determines the Lie algebra of any vector space then? For example we try the Lie algebra of horizontal space.

HallsofIvy

You seem to have the idea that there is such a thing as "the" Lie Algebra of a vector space. That's not true. There exist an infinite number of Lie Algebras for a given vector space.

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math6	lie algebra Tweet hi friends !! it is well known that a Lie algebra over K is a K-vector space g equipped of a K-bilinear, called Lie bracket. I ask how can we determines the Lie algebra of any vector space then? For example we try the Lie algebra of horizontal space.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	You seem to have the idea that there is such a thing as "the" Lie Algebra of a vector space. That's not true. There exist an infinite number of Lie Algebras for a given vector space.