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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)

Abstract

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.

Keywords

Associative Algebra Ring Homomorphism Algebraic Construction Casimir Element Invariant Bilinear Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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