Poincaré–Birkhoff–Witt theorem
Explicitly describes the universal enveloping algebra of a Lie algebra / From Wikipedia, the free encyclopedia
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For the Poincaré–Birkhoff fixed-point theorem, see Poincaré–Birkhoff theorem.
In mathematics, more specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie algebra. It is named after Henri Poincaré, Garrett Birkhoff, and Ernst Witt.
The terms PBW type theorem and PBW theorem may also refer to various analogues of the original theorem, comparing a filtered algebra to its associated graded algebra, in particular in the area of quantum groups.