dc.date.accessioned | 2020-04-28T18:40:27Z | |
dc.date.available | 2020-04-28T18:40:27Z | |
dc.date.created | 2019-07-08T17:45:51Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Kwasniewski, Bartosz K. Larsen, Nadia S. . Nica-Toeplitz algebras associated with right-tensor C*-precategories over right LCM semigroups. International Journal of Mathematics. 2019, 30(2) | |
dc.identifier.uri | http://hdl.handle.net/10852/74925 | |
dc.description.abstract | We introduce and analyze the full [Formula: see text] and the reduced [Formula: see text] Nica–Toeplitz algebra associated to an ideal [Formula: see text] in a right-tensor [Formula: see text]-precategory [Formula: see text] over a right LCM semigroup [Formula: see text]. These [Formula: see text]-algebras unify cross-sectional [Formula: see text]-algebras associated to Fell bundles over discrete groups and Nica–Toeplitz [Formula: see text]-algebras associated to product systems. They also allow a study of Doplicher–Roberts versions of the latter. A new phenomenon is that when [Formula: see text] is not right cancellative then the canonical conditional expectation takes values outside the ambient algebra. Our main result is a uniqueness theorem that gives sufficient conditions for a representation of [Formula: see text] to generate a [Formula: see text]-algebra naturally lying between [Formula: see text] and [Formula: see text]. We also characterize the situation when [Formula: see text]. Unlike previous results for quasi-lattice monoids, [Formula: see text] is allowed to contain nontrivial invertible elements, and we accommodate this by identifying an assumption of aperiodicity of an action of the group of invertible elements in [Formula: see text]. One prominent condition for uniqueness is a geometric condition of Coburn’s type, exploited in the work of Fowler, Laca and Raeburn. Here we shed new light on the role of this condition by relating it to a [Formula: see text]-algebra associated to [Formula: see text] itself. | |
dc.language | EN | |
dc.title | Nica-Toeplitz algebras associated with right-tensor C*-precategories over right LCM semigroups | |
dc.type | Journal article | |
dc.creator.author | Kwasniewski, Bartosz K. | |
dc.creator.author | Larsen, Nadia S. | |
cristin.unitcode | 185,15,13,65 | |
cristin.unitname | Flere komplekse variable, logikk og operatoralgebraer | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 1710700 | |
dc.identifier.bibliographiccitation | info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International Journal of Mathematics&rft.volume=30&rft.spage=&rft.date=2019 | |
dc.identifier.jtitle | International Journal of Mathematics | |
dc.identifier.volume | 30 | |
dc.identifier.issue | 02 | |
dc.identifier.doi | https://doi.org/10.1142/S0129167X19500137 | |
dc.identifier.urn | URN:NBN:no-78035 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0129-167X | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/74925/1/Nica-Toeplitz%2Balgebras%2Brevised17-01-2019.pdf | |
dc.type.version | AcceptedVersion | |
cristin.articleid | 1950013 | |