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Preprints, Working Papers, ... Year : 2020

Three variations on the linear independence of grouplikes in a coalgebra.

Trois variations sur l'indépendance linéaire des éléments de type groupe dans une cogèbre.

Darij Grinberg
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Vincel Hoang Ngoc Minh
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Abstract

The grouplike elements of a coalgebra over a field are known to be linearly independent over said field. Here we prove three variants of this result. One is a generalization to coalgebras over a commutative ring (in which case the linear independence has to be replaced by a weaker statement). Another is a stronger statement that holds (un-der stronger assumptions) in a commutative bialgebra. The last variant is a linear independence result for characters (as opposed to grouplike elements) of a bialgebra.
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Dates and versions

hal-02943601 , version 1 (20-09-2020)
hal-02943601 , version 2 (22-09-2020)
hal-02943601 , version 3 (23-02-2021)
hal-02943601 , version 4 (20-03-2021)
hal-02943601 , version 5 (01-08-2021)

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  • HAL Id : hal-02943601 , version 1

Cite

Gérard Henry Edmond Duchamp, Darij Grinberg, Vincel Hoang Ngoc Minh. Three variations on the linear independence of grouplikes in a coalgebra.. 2020. ⟨hal-02943601v1⟩
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