A cellular algebra with certain idempotent decomposition
| dc.creator | Wada, Kentaro | |
| dc.date | 2008-05-08 | |
| dc.date.accessioned | 2026-07-07T09:37:44Z | |
| dc.date.available | 2026-07-07T09:37:44Z | |
| dc.description | For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a decomposition of the unit element $1_\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular basis $\ZC$ can be partitioned into some pieces with good properties. Then by using a certain map $\a$, we give a coarse partition of $\ZC$ whose refinement is the original partition. We construct a Levi type subalgebra $\aA$ of $\A$ and its quotient algebra $\oA$, and also construct a parabolic type subalgebra $\tA$ of $\A$, which contains $\aA$ with respect to the map $\a$. Then, we study the relation of standard modules, simple modules and decomposition numbers among these algebras. Finally, we study the relationship of blocks among these algebras. | |
| dc.description | 37pages | |
| dc.identifier | https://arxiv.org/abs/0805.1147 | |
| dc.identifier | http://arxiv.org/abs/0805.1147 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160564 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C08, 20C20, 20G05 | |
| dc.title | A cellular algebra with certain idempotent decomposition | |
| dc.type | text |