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

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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https://hal.archives-ouvertes.fr/hal-02943601
Contributor : Gérard Duchamp <>
Submitted on : Tuesday, September 22, 2020 - 8:44:15 PM
Last modification on : Friday, September 25, 2020 - 3:27:51 AM

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  • HAL Id : hal-02943601, version 2
  • ARXIV : 2009.10970

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Gérard Duchamp, Darij Grinberg, Vincel Hoang Ngoc Minh. Three variations on the linear independence of grouplikes in a coalgebra.. 2020. ⟨hal-02943601v2⟩

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