Dilation Theory for Rank 2 Graph Algebras
| dc.creator | Davidson, Kenneth R. | |
| dc.creator | Power, Stephen C. | |
| dc.creator | Yang, Dilian | |
| dc.date | 2007-05-31 | |
| dc.date.accessioned | 2026-07-07T08:03:39Z | |
| dc.date.available | 2026-07-07T08:03:39Z | |
| dc.description | An analysis is given of $*$-representations of rank 2 single vertex graphs. We develop dilation theory for the non-selfadjoint algebras $\A_θ$ and $\A_u$ which are associated with the commutation relation permutation $θ$ of a 2 graph and, more generally, with commutation relations determined by a unitary matrix $u$ in $M_m(\bC) \otimes M_n(\bC)$. We show that a defect free row contractive representation has a unique minimal dilation to a $*$-representation and we provide a new simpler proof of Solel's row isometric dilation of two $u$-commuting row contractions. Furthermore it is shown that the C*-envelope of $\A_u$ is the generalised Cuntz algebra $Ø_{X_u}$ for the product system $X_u$ of $u$; that for $m\geq 2 $ and $n \geq 2 $ contractive representations of $\Ath$ need not be completely contractive; and that the universal tensor algebra $\T_+(X_u)$ need not be isometrically isomorphic to $\A_u$. | |
| dc.description | 29 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0705.4496 | |
| dc.identifier | http://arxiv.org/abs/0705.4496 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129659 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47L55 | |
| dc.title | Dilation Theory for Rank 2 Graph Algebras | |
| dc.type | text |