Blocks of Mackey categories
| dc.citation.epage | 57 | en_US |
| dc.citation.spage | 34 | en_US |
| dc.citation.volumeNumber | 446 | en_US |
| dc.contributor.author | Barker, L. | en_US |
| dc.date.accessioned | 2016-02-08T09:54:34Z | |
| dc.date.available | 2016-02-08T09:54:34Z | |
| dc.date.issued | 2016 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | For a suitable small category F of homomorphisms between finite groups, we introduce two subcategories of the biset category, namely, the deflation Mackey category MF← and the inflation Mackey category MF→. Let G be the subcategory of F consisting of the injective homomorphisms. We shall show that, for a field K of characteristic zero, the K-linear category KMG=KMG←=KMG→ has a semisimplicity property and, in particular, every block of KMG owns a unique simple functor up to isomorphism. On the other hand, we shall show that, when F is equivalent to the category of finite groups, the K-linear categories KMF← and KMF→ each have a unique block. © 2015 Elsevier Inc. | en_US |
| dc.identifier.doi | 10.1016/j.jalgebra.2015.09.002 | en_US |
| dc.identifier.eissn | 1090-266X | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/11693/22036 | |
| dc.language.iso | English | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1016/j.jalgebra.2015.09.002 | en_US |
| dc.source.title | Journal of Algebra | en_US |
| dc.subject | Biset category | en_US |
| dc.subject | Block of a linear category | en_US |
| dc.subject | Locally semisimple | en_US |
| dc.subject | Mackey system | en_US |
| dc.title | Blocks of Mackey categories | en_US |
| dc.type | Article | en_US |
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