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.
From: Darij Grinberg [view email] [via CCSD proxy]
[v1]
Wed, 23 Sep 2020 07:21:09 UTC (46 KB)
[v2]
Tue, 23 Feb 2021 08:57:40 UTC (50 KB)
[v3]
Mon, 22 Mar 2021 14:16:13 UTC (50 KB)
[v4]
Mon, 2 Aug 2021 14:20:44 UTC (50 KB)
[v5]
Fri, 3 Jul 2026 00:36:42 UTC (55 KB)
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