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<p>We consider the universal additive category derived from the category of equivariant separable <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2024_412_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras by introducing homotopy invariance, stability and split-exactness. We show that morphisms in that category permit a particular simple form, thus obtaining the universal property of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2024_412_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(KK^G\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <msup> <mi>K</mi> <mi>G</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>-theory for <i>G</i> a locally compact group, or a locally compact groupoid with compact base space, or a countable inverse semigroup as a byproduct.</p>

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Aspects of equivariant KK-theory in its generators and relations picture

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Bernhard Burgstaller

摘要

We consider the universal additive category derived from the category of equivariant separable \(C^*\) C ∗ -algebras by introducing homotopy invariance, stability and split-exactness. We show that morphisms in that category permit a particular simple form, thus obtaining the universal property of \(KK^G\) K K G -theory for G a locally compact group, or a locally compact groupoid with compact base space, or a countable inverse semigroup as a byproduct.