On the center of a compact group
| dc.creator | Mueger, Michael | |
| dc.date | 2003-12-12 | |
| dc.date | 2004-04-20 | |
| dc.date.accessioned | 2026-07-07T05:03:52Z | |
| dc.date.available | 2026-07-07T05:03:52Z | |
| dc.description | We prove a conjecture due to Baumgaertel and Lledo according to which for every compact group G one has Z(G)^ \cong C(G), where the `chain group' C(G) is the free abelian group (written multiplicatively) generated by the set G^ of isomorphism classes of irreducible representations of G modulo the relations [Z]=[X]\cdot[Y] whenever Z is contained in X \otimes Y. Thus the center Z(G) depends only on the representation ring of G. Furthermore, we prove that every `t-map' phi: G^ -> A into an abelian group, i.e. every map satisfying phi(Z)=phi(X)phi(Y) whenever X,Y,Z in G^ and Z\prec X\otimes Y, factors through the restriction map G^ -> Z(G)^. All these results also hold for proalgebraic groups over algebraically closed fields of characteristic zero. | |
| dc.description | Some improvements of terminology. Final version, to appear in I.M.R.N. latex2e, 6 pages, uses diagrams.tex | |
| dc.identifier | https://arxiv.org/abs/math/0312257 | |
| dc.identifier | http://arxiv.org/abs/math/0312257 | |
| dc.identifier | Int. Math. Res. Notices 2004, no. 51, 2751-2756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69585 | |
| dc.subject | Group Theory | |
| dc.subject | Category Theory | |
| dc.subject | 20E34; 18D10 | |
| dc.title | On the center of a compact group | |
| dc.type | text |