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<p>The aim of this article is to describe the form of Lie(Jordan) <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizers of triangular algebras, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> is an automorphism of triangular algebras. More precisely, we obtain that under mild conditions, every Lie <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizer can be written as the sum of a <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizer and a central-valued mapping and every Jordan <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizer of triangular algebras is a <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizer. As applications, Lie(Jordan) <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-centralizers on upper triangular matrix algebras and nest algebras are totally determined. At the same time, we also generalized the results.</p>

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Centralizers with automorphisms of triangular algebras

  • 期刊论文

  • 发表日期：

    2025年5月8日

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  • Xinfeng Liang,
  • Minghao Wang,
  • Mengya Zhang

摘要

The aim of this article is to describe the form of Lie(Jordan) \(\sigma \) σ -centralizers of triangular algebras, where \(\sigma \) σ is an automorphism of triangular algebras. More precisely, we obtain that under mild conditions, every Lie \(\sigma \) σ -centralizer can be written as the sum of a \(\sigma \) σ -centralizer and a central-valued mapping and every Jordan \(\sigma \) σ -centralizer of triangular algebras is a \(\sigma \) σ -centralizer. As applications, Lie(Jordan) \(\sigma \) σ -centralizers on upper triangular matrix algebras and nest algebras are totally determined. At the same time, we also generalized the results.