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W2109403554 abstract "To a special embedding <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Phi> <mml:semantics> <mml:mi mathvariant=normal>Φ</mml:mi> <mml:annotation encoding=application/x-tex>Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper C Superscript asterisk> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>C</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>mathbf {C}^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-algebra, denoted <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O Subscript normal upper Phi> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>Φ</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>mathcal {O}_{Phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, is a continuous version of the Cuntz-Krieger algebras <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O Subscript upper A> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:mi>A</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathcal {O}_A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O Subscript normal upper Phi> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>Φ</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>mathcal {O}_{Phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is generated by an A<bold>T</bold>-algebra and a nonunitary isometry. We compute its K-theory under the assumption that the A<bold>T</bold>-algebra is simple." @default.
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W2109403554 date "1996-01-01" @default.
W2109403554 modified "2023-10-12" @default.
W2109403554 title "Generalized Cuntz-Krieger algebras" @default.
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