Matches in SemOpenAlex for { <https://semopenalex.org/work/W2771524889> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W2771524889 abstract "A C*-algebra $A$ is said to be stable if it is isomorphic to $A otimes K(ell_2)$. Hjelmborg and Rordam have shown that countable inductive limits of separable stable C*-algebras are stable. We show that this is no longer true in the nonseparable context even for the most natural case of an uncountable inductive limit of an increasing chain of separable stable and AF ideals: we construct a GCR, AF (in fact, scattered) subalgebra $A$ of $B(ell_2)$, which is the inductive limit of length $omega_1$ of its separable stable ideals $I_alpha$ ($alpha<omega_1$) satisfying $I_{alpha+1}/I_alphacong K(ell_2)$ for each $alpha<omega_1$, while $A$ is not stable. The sequence $(I_alpha)_{alphaleqomega_1}$ is the GCR composition series of $A$ which in this case coincides with the Cantor-Bendixson composition series as a scattered C*-algebra. $A$ has the property that all of its proper two-sided ideals are listed as $I_alpha$s for some $alpha<omega_1$ and therefore the family of stable ideals of $A$ has no maximal element. By taking $A'=Aotimes K(ell_2)$ we obtain a stable C*-algebra with analogous composition series $(J_alpha)_{alpha<omega_1}$ whose ideals $J_alpha$s are isomorphic to $I_alpha$s for each $alpha<omega_1$. In particular, there are nonisomorphic scattered C*-algebras whose GCR composition series $(I_alpha)_{alphaleqomega_1}$ satisfy $I_{alpha+1}/I_alphacong K(ell_2)$ for all $alpha<omega_1$, for which the composition series differ first at $alpha=omega_1$." @default.
- W2771524889 created "2017-12-22" @default.
- W2771524889 creator A5019291245 @default.
- W2771524889 creator A5072763961 @default.
- W2771524889 date "2017-12-06" @default.
- W2771524889 modified "2023-09-25" @default.
- W2771524889 title "A non-stable C*-algebra with an elementary essential composition series" @default.
- W2771524889 cites W1527476078 @default.
- W2771524889 cites W153850935 @default.
- W2771524889 cites W1546322230 @default.
- W2771524889 cites W1565238249 @default.
- W2771524889 cites W1982306062 @default.
- W2771524889 cites W2003173901 @default.
- W2771524889 cites W2015365330 @default.
- W2771524889 cites W2034127031 @default.
- W2771524889 cites W2058318001 @default.
- W2771524889 cites W2061800462 @default.
- W2771524889 cites W2067662063 @default.
- W2771524889 cites W2072615684 @default.
- W2771524889 cites W2152703935 @default.
- W2771524889 cites W2276957906 @default.
- W2771524889 cites W2496530557 @default.
- W2771524889 cites W2598483411 @default.
- W2771524889 cites W2742046838 @default.
- W2771524889 cites W3099066709 @default.
- W2771524889 cites W634797762 @default.
- W2771524889 cites W2764353784 @default.
- W2771524889 hasPublicationYear "2017" @default.
- W2771524889 type Work @default.
- W2771524889 sameAs 2771524889 @default.
- W2771524889 citedByCount "2" @default.
- W2771524889 countsByYear W27715248892019 @default.
- W2771524889 countsByYear W27715248892020 @default.
- W2771524889 crossrefType "posted-content" @default.
- W2771524889 hasAuthorship W2771524889A5019291245 @default.
- W2771524889 hasAuthorship W2771524889A5072763961 @default.
- W2771524889 hasConcept C110729354 @default.
- W2771524889 hasConcept C114614502 @default.
- W2771524889 hasConcept C121332964 @default.
- W2771524889 hasConcept C134306372 @default.
- W2771524889 hasConcept C136119220 @default.
- W2771524889 hasConcept C138885662 @default.
- W2771524889 hasConcept C142399903 @default.
- W2771524889 hasConcept C143724316 @default.
- W2771524889 hasConcept C151730666 @default.
- W2771524889 hasConcept C202444582 @default.
- W2771524889 hasConcept C2779557605 @default.
- W2771524889 hasConcept C33923547 @default.
- W2771524889 hasConcept C40231798 @default.
- W2771524889 hasConcept C41895202 @default.
- W2771524889 hasConcept C62520636 @default.
- W2771524889 hasConcept C67996461 @default.
- W2771524889 hasConcept C70710897 @default.
- W2771524889 hasConcept C86803240 @default.
- W2771524889 hasConceptScore W2771524889C110729354 @default.
- W2771524889 hasConceptScore W2771524889C114614502 @default.
- W2771524889 hasConceptScore W2771524889C121332964 @default.
- W2771524889 hasConceptScore W2771524889C134306372 @default.
- W2771524889 hasConceptScore W2771524889C136119220 @default.
- W2771524889 hasConceptScore W2771524889C138885662 @default.
- W2771524889 hasConceptScore W2771524889C142399903 @default.
- W2771524889 hasConceptScore W2771524889C143724316 @default.
- W2771524889 hasConceptScore W2771524889C151730666 @default.
- W2771524889 hasConceptScore W2771524889C202444582 @default.
- W2771524889 hasConceptScore W2771524889C2779557605 @default.
- W2771524889 hasConceptScore W2771524889C33923547 @default.
- W2771524889 hasConceptScore W2771524889C40231798 @default.
- W2771524889 hasConceptScore W2771524889C41895202 @default.
- W2771524889 hasConceptScore W2771524889C62520636 @default.
- W2771524889 hasConceptScore W2771524889C67996461 @default.
- W2771524889 hasConceptScore W2771524889C70710897 @default.
- W2771524889 hasConceptScore W2771524889C86803240 @default.
- W2771524889 hasLocation W27715248891 @default.
- W2771524889 hasOpenAccess W2771524889 @default.
- W2771524889 hasPrimaryLocation W27715248891 @default.
- W2771524889 hasRelatedWork W1234549426 @default.
- W2771524889 hasRelatedWork W153850935 @default.
- W2771524889 hasRelatedWork W1901126459 @default.
- W2771524889 hasRelatedWork W1966428556 @default.
- W2771524889 hasRelatedWork W1978275127 @default.
- W2771524889 hasRelatedWork W2024119920 @default.
- W2771524889 hasRelatedWork W2263099264 @default.
- W2771524889 hasRelatedWork W2594228161 @default.
- W2771524889 hasRelatedWork W2790894077 @default.
- W2771524889 hasRelatedWork W2949272814 @default.
- W2771524889 hasRelatedWork W2949377676 @default.
- W2771524889 hasRelatedWork W2949949260 @default.
- W2771524889 hasRelatedWork W2950541119 @default.
- W2771524889 hasRelatedWork W2950675134 @default.
- W2771524889 hasRelatedWork W2951551410 @default.
- W2771524889 hasRelatedWork W2952906647 @default.
- W2771524889 hasRelatedWork W2962802782 @default.
- W2771524889 hasRelatedWork W3091988344 @default.
- W2771524889 hasRelatedWork W3167361675 @default.
- W2771524889 hasRelatedWork W989408151 @default.
- W2771524889 isParatext "false" @default.
- W2771524889 isRetracted "false" @default.
- W2771524889 magId "2771524889" @default.
- W2771524889 workType "article" @default.