DC Element | Wert | Sprache |
dc.contributor.author | JORGENSEN, PET | |
dc.contributor.author | SCHMITT, LM | |
dc.contributor.author | WERNER, RF | |
dc.date.accessioned | 2021-12-23T16:07:11Z | - |
dc.date.available | 2021-12-23T16:07:11Z | - |
dc.date.issued | 1994 | |
dc.identifier.issn | 00308730 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/7750 | - |
dc.description.abstract | We consider the q-deformed canonical commutation relations a(i)a(j)* - qa(j)*a(i) = delta(ij)1, i, j = 1, ..., d, where d is an integer, and - 1 < q < 1 . We show the existence of a universal solution of these relations, realized in a C*-algebra E(q) with the property that every other realization of the relations by bounded operators is a homomorphic image of the universal one. For q = 0 this algebra is the Cuntz algebra extended by an ideal isomorphic to the compact operators, also known as the Cuntz-Toeplitz algebra. We show that for a general class of commutation relations of the form a(i)a(j)* = GAMMA(ij)(a1 ,..., a(d)) with GAMMA an invertible matrix the algebra of the universal solution exists and is equal to the Cuntz-Toeplitz algebra. For the particular case of the q-canonical commutation relations this result applies for Absolute value of q < square-root 2 - 1 . Hence for these values E(q) is isomorphic to E0. The example a(i)a(j)* - qa(i)*a(j) = delta(ij)1 is also treated in detail. | |
dc.language.iso | en | |
dc.publisher | PACIFIC JOURNAL MATHEMATICS | |
dc.relation.ispartof | PACIFIC JOURNAL OF MATHEMATICS | |
dc.subject | BOSE STATISTICS | |
dc.subject | CSTAR-ALGEBRAS | |
dc.subject | EXAMPLE | |
dc.subject | FERMI | |
dc.subject | Mathematics | |
dc.subject | OSCILLATOR | |
dc.title | Q-CANONICAL COMMUTATION RELATIONS AND STABILITY OF THE CUNTZ ALGEBRA | |
dc.type | journal article | |
dc.identifier.doi | 10.2140/pjm.1994.165.131 | |
dc.identifier.isi | ISI:A1994PC16300008 | |
dc.description.volume | 165 | |
dc.description.issue | 1 | |
dc.description.startpage | 131 | |
dc.description.endpage | 151 | |
dc.contributor.orcid | 0000-0003-2288-468X | |
dc.contributor.orcid | 0000-0003-2681-5753 | |
dc.contributor.researcherid | C-1123-2009 | |
dc.publisher.place | PO BOX 4163, BERKELEY, CA 94704-0163 | |
dcterms.isPartOf.abbreviation | Pac. J. Math. | |
dcterms.oaStatus | Bronze, Green Submitted | |