The Universal Enveloping Algebra
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.
KeywordsAssociative Algebra Ring Homomorphism Algebraic Construction Casimir Element Invariant Bilinear Form
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