On Frobenius and separable Galois cowreaths
We show that a Galois cowreath ( A , X ) in a monoidal category C is Frobenius if and only if the subalgebra of coinvariants A co ( X ) ↪ A is a Frobenius algebra extension in C . Then we give necessary and sufficient conditions for A co ( X ) ↪ A to be separable, and prove that a Frobenius Galois...
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| Veröffentlicht in: | Mathematische Zeitschrift 2021-02, Vol.297 (1-2), p.25-57 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that a Galois cowreath (
A
,
X
) in a monoidal category
C
is Frobenius if and only if the subalgebra of coinvariants
A
co
(
X
)
↪
A
is a Frobenius algebra extension in
C
. Then we give necessary and sufficient conditions for
A
co
(
X
)
↪
A
to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral. |
|---|---|
| ISSN: | 0025-5874 1432-1823 |
| DOI: | 10.1007/s00209-020-02495-8 |