• 제목/요약/키워드: Upper triangular matrix Lie algebras

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STRONG COMMUTATIVITY PRESERVING MAPS OF UPPER TRIANGULAR MATRIX LIE ALGEBRAS OVER A COMMUTATIVE RING

  • Chen, Zhengxin;Zhao, Yu'e
    • 대한수학회보
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    • 제58권4호
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    • pp.973-981
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    • 2021
  • Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯n(R).