dc.contributor.author | Shelley-Abrahamson, Seth | |
dc.date.accessioned | 2017-03-16T20:20:36Z | |
dc.date.available | 2017-04-11T21:29:35Z | |
dc.date.issued | 2016-06 | |
dc.date.submitted | 2015-08 | |
dc.identifier.issn | 1386-923X | |
dc.identifier.issn | 1572-9079 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/107447 | |
dc.description.abstract | For a finite group G and nonnegative integer n ≥ 0, one may consider the associated tower G≀S[subscript n]:=S[subscript n]⋉G[superscript n] of wreath product groups. Zelevinsky associated to such a tower the structure of a positive self-adjoint Hopf algebra (PSH-algebra) R(G) on the direct sum over integers n ≥ 0 of the Grothendieck groups K[subscript 0](Rep−G≀S[subscript n]). In this paper, we study the interaction via induction and restriction of the PSH-algebras R(G) and R(H) associated to finite groups H ⊂ G. A class of Hopf modules over PSH-algebras with a compatibility between the comultiplication and multiplication involving the Hopf k[superscript th]-power map arise naturally and are studied independently. We also give an explicit formula for the natural PSH-algebra morphisms R(H) → R(G) and R(G) → R(H) arising from induction and restriction. In an appendix, we consider a family of subgroups of wreath product groups analogous to the subgroups G(m, p, n) of the wreath product cyclotomic complex reflection groups G(m, 1, n). | en_US |
dc.publisher | Springer Netherlands | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s10468-016-9633-4 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | Springer Netherlands | en_US |
dc.title | Hopf Modules and Representations of Finite Wreath Products | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Shelley-Abrahamson, Seth. “Hopf Modules and Representations of Finite Wreath Products.” Algebras and Representation Theory 20, no. 1 (June 29, 2016): 123–145. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Shelley-Abrahamson, Seth | |
dc.relation.journal | Algebras and Representation Theory | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2017-02-08T04:30:10Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer Science+Business Media Dordrecht | |
dspace.orderedauthors | Shelley-Abrahamson, Seth | en_US |
dspace.embargo.terms | N | en |
dc.identifier.orcid | https://orcid.org/0000-0002-9807-1805 | |
mit.license | PUBLISHER_POLICY | en_US |