| 1. | This derivation extends to the universal enveloping algebra of the Lie algebra.
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| 2. | The universal enveloping algebra is obtained by modding out the Poisson algebra structure.
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| 3. | Quantum deformations of the universal enveloping algebra lead to the notion of quantum groups.
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| 4. | The usual algebraic proof makes use of the Casimir element of the universal enveloping algebra.
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| 5. | Conversely to any Lie algebra there is a corresponding ring, called the universal enveloping algebra.
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| 6. | This is analogous to looking at the center of the universal enveloping algebra of a Lie algebra.
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| 7. | The universal enveloping algebra of a Lie algebra \ mathfrak { g } is also naturally filtered.
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| 8. | For example, the enveloping algebra of a complex Lie algebra is almost commutative by the PBW theorem.
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| 9. | With Masaki Kashiwara, she formulated a conjecture about the combinatorial structure of the enveloping algebras of Lie algebras.
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| 10. | Over the rationals this identifies the Hopf algebra NSYmm with the universal enveloping algebra of the free Lie algebra.
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मोबाइल