Abstract
We prove that there exist Hopf algebras with surjective antipode which admit no nontrivial morphisms from Hopf algebras with bijective antipode; in particular, they are not quotients of such. This answers a question left open in prior work, and contrasts with the dual setup whereby a Hopf algebra has injective antipode precisely when it embeds into one with bijective antipode.
| Original language | English |
|---|---|
| Article number | 2550056 |
| Journal | International Journal of Mathematics |
| Volume | 36 |
| Issue number | 13 |
| DOIs | |
| State | Published - Nov 1 2025 |
Keywords
- Diamond lemma
- Tannaka reconstruction
- adjoint functor
- antipode
- comodule
- free Hopf algebra
- subquotient
- triangular
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