FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3169577447> ?p ?o ?g. }

• W3169577447 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma normal upper Gamma right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X, Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a free and minimal topological dynamical system, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a separable compact Hausdorff space and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Gamma> <mml:semantics> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:annotation encoding=application/x-tex>Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a countable infinite discrete amenable group. It is shown that if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma normal upper Gamma right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X, Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has the Uniform Rokhlin Property (URP) and Cuntz comparison of open sets (COS), then <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal m normal d normal i normal m left-parenthesis upper X comma normal upper Gamma right-parenthesis equals 0> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>m</mml:mi> <mml:mi mathvariant=normal>d</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>m</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {mdim}(X, Gamma )=0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> implies that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis normal upper C left-parenthesis upper X right-parenthesis right-normal-factor-semidirect-product normal upper Gamma right-parenthesis circled-times script upper Z approximately-equals normal upper C left-parenthesis upper X right-parenthesis right-normal-factor-semidirect-product normal upper Gamma> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>Z</mml:mi> </mml:mrow> <mml:mo>≅<!-- ≅ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>(mathrm {C}(X) rtimes Gamma )otimes mathcal Z cong mathrm {C}(X) rtimes Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal m normal d normal i normal m> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>m</mml:mi> <mml:mi mathvariant=normal>d</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>m</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {mdim}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the mean dimension of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma normal upper Gamma right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X, Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper Z> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>Z</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the Jiang-Su algebra, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper C left-parenthesis upper X right-parenthesis right-normal-factor-semidirect-product normal upper Gamma> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {C}(X) rtimes Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the transformation group C*-algebra of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma normal upper Gamma right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X, Gamma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In particular, in this case, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal m normal d normal i normal m left-parenthesis upper X comma normal upper Gamma right-parenthesis equals 0> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>m</mml:mi> <mml:mi mathvariant=normal>d</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>m</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {mdim}(X, Gamma )=0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> implies that the C*-algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper C left-parenthesis upper X right-parenthesis right-normal-factor-semidirect-product normal upper Gamma> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>C</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {C}(X) rtimes Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is classified by the Elliott invariant." @default.
• W3169577447 created "2021-06-22" @default.
• W3169577447 creator A5047074100 @default.
• W3169577447 date "2021-07-19" @default.
• W3169577447 modified "2023-10-16" @default.
• W3169577447 title "$mathcal {Z}$-stability of transformation group C*-algebras" @default.
• W3169577447 cites W1563826039 @default.
• W3169577447 cites W1700841590 @default.
• W3169577447 cites W187295716 @default.
• W3169577447 cites W1983946282 @default.
• W3169577447 cites W1989318995 @default.
• W3169577447 cites W2018662664 @default.
• W3169577447 cites W2046045869 @default.
• W3169577447 cites W2062803982 @default.
• W3169577447 cites W2070509948 @default.
• W3169577447 cites W2071297813 @default.
• W3169577447 cites W2072401907 @default.
• W3169577447 cites W2126727921 @default.
• W3169577447 cites W2140792325 @default.
• W3169577447 cites W2248394449 @default.
• W3169577447 cites W2263898306 @default.
• W3169577447 cites W2592309116 @default.
• W3169577447 cites W2910591674 @default.
• W3169577447 cites W2962904304 @default.
• W3169577447 cites W2963048041 @default.
• W3169577447 cites W2963183166 @default.
• W3169577447 cites W2963334269 @default.
• W3169577447 cites W2963459424 @default.
• W3169577447 cites W2963819596 @default.
• W3169577447 cites W2963821633 @default.
• W3169577447 cites W2964082912 @default.
• W3169577447 cites W2964256349 @default.
• W3169577447 cites W3048905068 @default.
• W3169577447 cites W3098491911 @default.
• W3169577447 cites W3098866972 @default.
• W3169577447 cites W3098994277 @default.
• W3169577447 cites W3099031657 @default.
• W3169577447 cites W3101051734 @default.
• W3169577447 cites W3104339251 @default.
• W3169577447 cites W3125669370 @default.
• W3169577447 doi "https://doi.org/10.1090/tran/8477" @default.
• W3169577447 hasPublicationYear "2021" @default.
• W3169577447 type Work @default.
• W3169577447 sameAs 3169577447 @default.
• W3169577447 citedByCount "1" @default.
• W3169577447 countsByYear W31695774472023 @default.
• W3169577447 crossrefType "journal-article" @default.
• W3169577447 hasAuthorship W3169577447A5047074100 @default.
• W3169577447 hasBestOaLocation W31695774471 @default.
• W3169577447 hasConcept C11413529 @default.
• W3169577447 hasConcept C154945302 @default.
• W3169577447 hasConcept C2776321320 @default.
• W3169577447 hasConcept C33923547 @default.
• W3169577447 hasConcept C41008148 @default.
• W3169577447 hasConceptScore W3169577447C11413529 @default.
• W3169577447 hasConceptScore W3169577447C154945302 @default.
• W3169577447 hasConceptScore W3169577447C2776321320 @default.
• W3169577447 hasConceptScore W3169577447C33923547 @default.
• W3169577447 hasConceptScore W3169577447C41008148 @default.
• W3169577447 hasFunder F4320306076 @default.
• W3169577447 hasLocation W31695774471 @default.
• W3169577447 hasOpenAccess W3169577447 @default.
• W3169577447 hasPrimaryLocation W31695774471 @default.
• W3169577447 hasRelatedWork W1490908374 @default.
• W3169577447 hasRelatedWork W151193258 @default.
• W3169577447 hasRelatedWork W1529400504 @default.
• W3169577447 hasRelatedWork W1607472309 @default.
• W3169577447 hasRelatedWork W1871911958 @default.
• W3169577447 hasRelatedWork W1892467659 @default.
• W3169577447 hasRelatedWork W2808586768 @default.
• W3169577447 hasRelatedWork W2998403542 @default.
• W3169577447 hasRelatedWork W3107474891 @default.
• W3169577447 hasRelatedWork W38394648 @default.
• W3169577447 isParatext "false" @default.
• W3169577447 isRetracted "false" @default.
• W3169577447 magId "3169577447" @default.
• W3169577447 workType "article" @default.