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arXiv · 2009.10970

Three variations on the linear independence of grouplikes in a coalgebra

Gérard Duchamp·Darij Grinberg·Vincel 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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Gérard Duchamp, Darij Grinberg, Vincel Minh. 2020-09-23. Three variations on the linear independence of grouplikes in a coalgebra. https://arxiv.org/abs/2009.10970

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