Subcoalgebras and endomorphisms of free Hopf algebras

Details Subcoalgebras and endomorphisms of free Hopf algebras Subcoalgebras and endomorphisms of free Hopf algebras

2010-02-17

arxiv.org/abs/1002.3198v2

Mathematics

Rings and Algebras

12 pages; corrected minor typos; to appear in J. Pure Appl. Algebra

Scientific paper

10.1016/j.jpaa.2010.04.002

For a matrix coalgebra $C$ over some field, we determine all small subcoalgebras of the free Hopf algebra on $C$, the free Hopf algebra with a bjective antipode on $C$, and the free Hopf algebra with antipode $S$ satisfying $S^{2d}={\rm id}$ on $C$ for some fixed $d$. We use this information to find the endomorphisms of these free Hopf algebras, and to determine the centers of the categories of Hopf algebras, Hopf algebras with bijective antipode, and Hopf algebras with antipode of order dividing 2d.

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