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Let \(\mathcal {A}\) be a unital \(*\) -algebra and \(\mathcal {L}=\{L_n\}_{n\in \textrm{N}}\) be a nonlinear \(*\) -Lie higher derivation on \(\mathcal {A}.\) In the present paper, it is shown that under some appropriate assumptions \(\mathcal {L}\) is proper, that is, for each \(n\in \textrm{N},\) \(L_n:\mathcal {A}\rightarrow \mathcal {A}\) has the form \(L_n=d_n+\tau _n,\) where \(\{d_n\}_{n\in \textrm{N} }\) is an additive \(*\) -higher derivation on \(\mathcal {A}\) and \(\{\tau _n\}_{n\in \textrm{N} }\) is a family of mappings \(\tau _n:\mathcal {A}\rightarrow \mathcal {Z(A)}\) such that \(\tau _n([x,y])=0\) for all \(x,y\in \mathcal {A},\) \(n\in \textrm{N}\) .

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Nonlinear \(*\) -Lie Higher Derivations of Unital \(*\) -Algebras

  • 会议论文

  • 发表日期：

    2025年

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  • Mohammad Ashraf,
  • Jehad Jumah Al Jaraden,
  • Mohammad Afajal Ansari,
  • Md Shamim Akhter

摘要

Let \(\mathcal {A}\) be a unital \(*\) -algebra and \(\mathcal {L}=\{L_n\}_{n\in \textrm{N}}\) be a nonlinear \(*\) -Lie higher derivation on \(\mathcal {A}.\) In the present paper, it is shown that under some appropriate assumptions \(\mathcal {L}\) is proper, that is, for each \(n\in \textrm{N},\) \(L_n:\mathcal {A}\rightarrow \mathcal {A}\) has the form \(L_n=d_n+\tau _n,\) where \(\{d_n\}_{n\in \textrm{N} }\) is an additive \(*\) -higher derivation on \(\mathcal {A}\) and \(\{\tau _n\}_{n\in \textrm{N} }\) is a family of mappings \(\tau _n:\mathcal {A}\rightarrow \mathcal {Z(A)}\) such that \(\tau _n([x,y])=0\) for all \(x,y\in \mathcal {A},\) \(n\in \textrm{N}\) .