Non-Commutative Vector Bundles for Non-Unital Algebras
We revisit the characterisation of modules over non-unital C∗-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module co...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148641 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Non-Commutative Vector Bundles for Non-Unital Algebras / A. Rennie, A. Sims // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862691758993833984 |
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| author | Rennie, A. Sims, A. |
| author_facet | Rennie, A. Sims, A. |
| citation_txt | Non-Commutative Vector Bundles for Non-Unital Algebras / A. Rennie, A. Sims // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 11 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We revisit the characterisation of modules over non-unital C∗-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module construction in the context of bi-Hilbertian bimodules, particularly those of finite numerical index and finite Watatani index.
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| first_indexed | 2025-12-07T16:16:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148641 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:16:54Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rennie, A. Sims, A. 2019-02-18T16:51:26Z 2019-02-18T16:51:26Z 2017 Non-Commutative Vector Bundles for Non-Unital Algebras / A. Rennie, A. Sims // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 11 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57R22; 46L85 DOI:10.3842/SIGMA.2017.041 https://nasplib.isofts.kiev.ua/handle/123456789/148641 We revisit the characterisation of modules over non-unital C∗-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module construction in the context of bi-Hilbertian bimodules, particularly those of finite numerical index and finite Watatani index. This research was supported by Australian Research Council grant DP150101595. It was motivated by questions arising in projects with our collaborators Francesca Arici, Magnus Gof feng,
 Bram Mesland and Dave Robertson, and we thank them for all that we have learned from
 them. We are very grateful to the anonymous referee who read the manuscript very closely and
 made numerous very helpful suggestions that have significantly strengthened our results and
 streamlined our proofs. Thanks, whoever you are. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Commutative Vector Bundles for Non-Unital Algebras Article published earlier |
| spellingShingle | Non-Commutative Vector Bundles for Non-Unital Algebras Rennie, A. Sims, A. |
| title | Non-Commutative Vector Bundles for Non-Unital Algebras |
| title_full | Non-Commutative Vector Bundles for Non-Unital Algebras |
| title_fullStr | Non-Commutative Vector Bundles for Non-Unital Algebras |
| title_full_unstemmed | Non-Commutative Vector Bundles for Non-Unital Algebras |
| title_short | Non-Commutative Vector Bundles for Non-Unital Algebras |
| title_sort | non-commutative vector bundles for non-unital algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148641 |
| work_keys_str_mv | AT renniea noncommutativevectorbundlesfornonunitalalgebras AT simsa noncommutativevectorbundlesfornonunitalalgebras |