<p>We describe <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2872_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-matching, interchangeable and, as a consequence, totally compatible structures on the strictly upper triangular matrix algebra <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2872_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(UT_n(K)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msub> <mi>T</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2872_Article_IEq6.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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\(\sigma \)-Matching and Interchangeable Structures on the Strictly Upper Triangular Matrix Algebra

  • Mykola Khrypchenko

摘要

We describe \(\sigma \) σ -matching, interchangeable and, as a consequence, totally compatible structures on the strictly upper triangular matrix algebra \(UT_n(K)\) U T n ( K ) for all \(n\ge 3\) n 3 .