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<p>We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5337_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_{8}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mn>8</mn> </msub> </math></EquationSource> </InlineEquation> subfactor on a noncommutative 3-torus, and of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="220_2025_5337_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {PSU}(2)_{15}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>PSU</mtext> <msub> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mn>15</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> on a noncommutative 4-torus.</p>

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Quantum Symmetries of Noncommutative Tori

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • David E. Evans,
  • Corey Jones

摘要

We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the \(E_{8}\) E 8 subfactor on a noncommutative 3-torus, and of \(\text {PSU}(2)_{15}\) PSU ( 2 ) 15 on a noncommutative 4-torus.