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<p>Given a separable, AF-algebra <i>A</i> and an inductive limit action on <i>A</i> of a finitely generated abelian group with finite Rokhlin dimension with commuting towers, we give a local description of the associated crossed product C*-algebra. In particular, when <i>A</i> is unital and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \in {{\,\mathrm{\textrm{Aut}}\,}}(A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mrow> <mspace width="0.166667em" /> <mtext>Aut</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is approximately inner and has the Rokhlin property, we conclude that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(A\rtimes _{\alpha } {\mathbb {Z}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>A</mi> <msub> <mo>⋊</mo> <mi>α</mi> </msub> <mi mathvariant="double-struck">Z</mi> </mrow> </math></EquationSource> </InlineEquation> is an A<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {T}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">T</mi> </math></EquationSource> </InlineEquation>-algebra.</p>

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Rokhlin dimension and inductive limit actions on AF-algebras

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Sureshkumar Mariappan,
  • Prahlad Vaidyanathan

摘要

Given a separable, AF-algebra A and an inductive limit action on A of a finitely generated abelian group with finite Rokhlin dimension with commuting towers, we give a local description of the associated crossed product C*-algebra. In particular, when A is unital and \(\alpha \in {{\,\mathrm{\textrm{Aut}}\,}}(A)\) α ∈ Aut ( A ) is approximately inner and has the Rokhlin property, we conclude that \(A\rtimes _{\alpha } {\mathbb {Z}}\) A ⋊ α Z is an A \({\mathbb {T}}\) T -algebra.