Central extensions of the Heisenberg algebra
| dc.creator | Accardi, Luigi | |
| dc.creator | Boukas, Andreas | |
| dc.date | 2008-10-19 | |
| dc.date.accessioned | 2026-07-07T10:11:34Z | |
| dc.date.available | 2026-07-07T10:11:34Z | |
| dc.description | We study the non-trivial central extensions $CEHeis$ of the Heisenberg algebra $Heis$ recently constructed in {AccBouCE}. We prove that a real form of $CEHeis$ is one the fifteen classified real four--dimensional solvable Lie algebras. We also show that $CEHeis$ can be realized (i) as a sub--Lie--algebra of the Schroedinger algebra and (ii) in terms of two independent copies of the canonical commutation relations (CCR). This gives a natural family of unitary representations of $CEHeis$ and allows an explicit determination of the associated group by exponentiation. In contrast with $Heis$, the group law for $CEHeis$ is given by nonlinear (quadratic) functions of the coordinates. | |
| dc.identifier | https://arxiv.org/abs/0810.3365 | |
| dc.identifier | http://arxiv.org/abs/0810.3365 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171901 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Probability | |
| dc.subject | 81S05, 60B15, 17B15 | |
| dc.title | Central extensions of the Heisenberg algebra | |
| dc.type | text |