| 11. | These include the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras.
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| 12. | By definition any member of the center of the universal enveloping algebra commutes with all other elements in the algebra.
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| 13. | Every Lie algebra can be embedded into one that arises from an associative algebra in this fashion; see universal enveloping algebra.
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| 14. | In common with all universal enveloping algebras, it has a natural structure of a Hopf algebra, with a coproduct ?.
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| 15. | Examples of this are the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras.
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| 16. | It is a special case of the &-product of the " algebra of symbols " of a universal enveloping algebra.
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| 17. | The article on universal enveloping algebras describes the canonical construction of enveloping algebras, as well as the PBW-type theorems for them.
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| 18. | The article on universal enveloping algebras describes the canonical construction of enveloping algebras, as well as the PBW-type theorems for them.
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| 19. | Like in the non-graded case, this Hopf algebra can be described purely algebraically as the universal enveloping algebra of the Lie superalgebra.
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| 20. | For Lie algebras, such enveloping algebras have a universal property, which does not hold, in general, for non-associative algebras.
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