Lie Groups pp 54-57 | Cite as

The Universal Enveloping Algebra

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


We have seen that elements of the Lie algebra of a Lie group G are derivations of C (G); that is, differential operators that are left-invariant. The universal enveloping algebra is the ring of all left-invariant differential operators, including higher-order ones. There is a purely algebraic construction of this ring.


Associative Algebra Ring Homomorphism Algebraic Construction Casimir Element Invariant Bilinear Form 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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