No-go theorems for functorial localic spectra of noncommutative rings
Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in...
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| Format: | Article |
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Open Publishing Association
2012-10-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1101.5924v3 |
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doaj-df67598cb0484fd1a06eea88c3ee96892020-11-24T23:11:16ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802012-10-0195Proc. QPL 2011212510.4204/EPTCS.95.3No-go theorems for functorial localic spectra of noncommutative ringsBenno van den BergChris HeunenAny functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in categories other than that of locales is briefly discussed.http://arxiv.org/pdf/1101.5924v3 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Benno van den Berg Chris Heunen |
| spellingShingle |
Benno van den Berg Chris Heunen No-go theorems for functorial localic spectra of noncommutative rings Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Benno van den Berg Chris Heunen |
| author_sort |
Benno van den Berg |
| title |
No-go theorems for functorial localic spectra of noncommutative rings |
| title_short |
No-go theorems for functorial localic spectra of noncommutative rings |
| title_full |
No-go theorems for functorial localic spectra of noncommutative rings |
| title_fullStr |
No-go theorems for functorial localic spectra of noncommutative rings |
| title_full_unstemmed |
No-go theorems for functorial localic spectra of noncommutative rings |
| title_sort |
no-go theorems for functorial localic spectra of noncommutative rings |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2012-10-01 |
| description |
Any functor from the category of C*-algebras to the category of locales that assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of nxn-matrices for n at least 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in categories other than that of locales is briefly discussed. |
| url |
http://arxiv.org/pdf/1101.5924v3 |
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AT bennovandenberg nogotheoremsforfunctoriallocalicspectraofnoncommutativerings AT chrisheunen nogotheoremsforfunctoriallocalicspectraofnoncommutativerings |
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