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<p>In this article we investigate the primeness of generalized wreath product <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2024_3666_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {II}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>II</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>factors using deformation/rigidity theory techniques. We give general conditions relating tensor decompositions of generalized wreath products to stabilizers of the associated group action and use this to find new examples of prime <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2024_3666_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {II}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>II</mtext> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>factors.</p>

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Primeness of generalized wreath product \(\hbox {II}_1\)factors

  • 期刊论文

  • 发表日期：

    2025年1月16日

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  • Gregory Patchell

摘要

In this article we investigate the primeness of generalized wreath product \(\hbox {II}_1\) II 1 factors using deformation/rigidity theory techniques. We give general conditions relating tensor decompositions of generalized wreath products to stabilizers of the associated group action and use this to find new examples of prime \(\hbox {II}_1\) II 1 factors.