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Representability of permutation representations on coalgebras and the isomorphism problem

Costoya, Cristina, Méndez, David and Viruel, Antonio (2020) Representability of permutation representations on coalgebras and the isomorphism problem. Mediterranean Journal of Mathematics, 17 (5), [157].

Record type: Article

Abstract

Let G be a group and let ρ: G → Sym(V ) be a permutation representation of G on a set V . We prove that there is a faithful G-coalgebra C such that G arises as the image of the restriction of Aut(C) to G(C), the set of grouplike elements of C. Furthermore, we show that V can be regarded as a subset of G(C) invariant through the G-action, and that the composition of the inclusion G ֒→ Aut(C) with the restriction Aut(C) → Sym(V ) is precisely ρ. We use these results to prove that isomorphism classes of certain families of groups can be distinguished through the coalgebras on which they act faithfully.

Text
1907.00626v1 - Accepted Manuscript

Accepted/In Press date: 1 July 2019
e-pub ahead of print date: 20 August 2020
Keywords: Primary 20G05, Secondary 05E18, 16T15, math.CO, math.RT

Identifiers

Local EPrints ID: 441369
URI: http://eprints.soton.ac.uk/id/eprint/441369
ISSN: 1660-5454
PURE UUID: f8bd30f9-ec92-4d5a-92dc-4a59f52da41b
ORCID for David Méndez: orcid.org/0000-0003-4023-172X

Catalogue record

Date deposited: 10 Jun 2020 16:31

Contributors

Author: Cristina Costoya
Author: David Méndez
Author: Antonio Viruel