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