Poincaré-Birkhoff-Witt Theorem

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

See also

Associative, Lie Algebra, Vector Space

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Jacobson, N. Lie Algebras. New York: Dover, pp. 159-160, 1979.Schafer, R. D. An Introduction to Nonassociative Algebras. New York: Dover, p. 3, 1996.

Referenced on Wolfram|Alpha

Poincaré-Birkhoff-Witt Theorem

Cite this as:

Weisstein, Eric W. "Poincaré-Birkhoff-Witt Theorem." From MathWorld--A Wolfram Web Resource.

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