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Poincaré–Birkhoff–Witt 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.

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Statement of the theorem

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History of the theorem

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Poincaré–Birkhoff–Witt theorem

Nodes34
Edges33
Triples30
Avg. degree1.94
Density0.058824
Components1

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Poincaré–Birkhoff–Witt theorem

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related to history · 21
Poincaré–Birkhoff–Witt theorem → Alfredo Capelli, Armand Borel, Birkhoff, Birkhoff-Witt, Bourbaki, Bourbaki's, Capelli, Capelli's, Fofanova, Following, General, In, It, Lie, Poincaré, Poincaré's, She, They, Ton-That, Tran
related to Statement of the theorem · 8
Poincaré–Birkhoff–Witt theorem → Birkhoff, If, In, K-linear, Lie, Poincaré, Recall, Witt

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theorem lie witt algebra poincaré birkhoff basis field one canonical groups isbn elements monomials doi mathematics displaystyle k-module 10 algebras

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SubjectPredicateObjectConfidenceSrc
whereinstance ofthe PBW theorem as formulated above extends to cases0.80text
Poincaré–Birkhoff–Witt theoremrelated to historyIn0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyAlfredo Capelli0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyPoincaré0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyBirkhoff0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyWitt0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyGeneral0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyLie0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyArmand Borel0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyCapelli0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyCapelli's0.60section
Poincaré–Birkhoff–Witt theoremrelated to historyTon-That0.60section

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    Researching Poincaré–Birkhoff–Witt theorem? Use this map to explore History, History of the theorem & Statement of the theorem and other closely related topics, then follow useful entities and relationships into deeper research. Automatically generated connections are research leads, so verify important facts in reliable sources.