Hopf theory MOC

Hopf ideal

Let be a Hopf algebra over . A Hopf ideal is a biïdeal which is additionally stable under the antipous, #m/def/ralg/hopf i.e. .

Theorem

Let be an ideal such that

and . Then any of the following ensure is a Hopf ideal:1

  1. is finitely generated as a -module.
  2. is Noetherian, and is Module-finite -monoid.
  3. is Noetherian, and is a Commutative -monoid of finite type.

If instead is a Hopf algebra over , then any of the following are sufficient.

  1. is commutative.
  2. is pointed.
  3. is cocommutative.
Proof

#missing/proof See op. cit.

#state/develop | #lang/en | #SemBr

Footnotes

  1. 1978. Quotients of Hopf algebras ↩