Three variations on the linear independence of grouplikes in a coalgebra
Quantum Algebra
2021-08-03 v4 Combinatorics
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.
Cite
@article{arxiv.2009.10970,
title = {Three variations on the linear independence of grouplikes in a coalgebra},
author = {Gérard Duchamp and Darij Grinberg and Vincel Minh},
journal= {arXiv preprint arXiv:2009.10970},
year = {2021}
}