<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {A}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">A</mi> </math></EquationSource> </InlineEquation> be a <InlineEquation ID="IEq4"> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-algebra. For any <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {A}, \mathscr {B}\in \mathcal {A}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">A</mi> <mo>,</mo> <mi mathvariant="script">B</mi> <mo>∈</mo> <mi mathvariant="script">A</mi> </mrow> </math></EquationSource> </InlineEquation>, the products <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$ \mathscr {A} \bullet \mathscr {B}=\mathscr {A}\mathscr {B}^+\mathscr {B}\mathscr {A}^$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">A</mi> <mo>∙</mo> <mi mathvariant="script">B</mi> <mo>=</mo> <mi mathvariant="script">A</mi> <msup> <mi mathvariant="script">B</mi> <mo>∗</mo> </msup> <mo>+</mo> <mi mathvariant="script">B</mi> <msup> <mi mathvariant="script">A</mi> <mo>∗</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$[\mathscr {A}, \mathscr {B}]_=\mathscr {A}\mathscr {B}^-\mathscr {B}\mathscr {A}^$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mo stretchy="false">[</mo> <mi mathvariant="script">A</mi> <mo>,</mo> <mi mathvariant="script">B</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </msub> <mo>=</mo> <mi mathvariant="script">A</mi> <msup> <mi mathvariant="script">B</mi> <mo>∗</mo> </msup> <mo>-</mo> <mi mathvariant="script">B</mi> <msup> <mi mathvariant="script">A</mi> <mo>∗</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> are called a bi-skew Jordan and bi-skew Lie product, respectively. In this paper, it is shown that every non-additive mixed bi-skew Jordan and bi-skew Lie triple derivation <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\Lambda : \mathcal {A}\rightarrow \mathcal {A}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mo>:</mo> <mi mathvariant="script">A</mi> <mo stretchy="false">→</mo> <mi mathvariant="script">A</mi> </mrow> </math></EquationSource> </InlineEquation> is an additive <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$*$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation.</p>

Non-additive mixed bi-skew Jordan and bi-skew Lie triple derivations on $*$-algebras

期刊论文
发表日期：

2026年3月2日

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Adnan Abbasi,
Mohd Saif,
Abdul Nadim Khan

摘要

Let $\mathcal {A}$ $A$ be a $*$ $*$ -algebra. For any $\mathcal {A}, \mathscr {B}\in \mathcal {A}$ $A, B \in A$ , the products $ \mathscr {A} \bullet \mathscr {B}=\mathscr {A}\mathscr {B}^*+\mathscr {B}\mathscr {A}^*$ $A ∙ B = A B^{*} + B A^{*}$ , $[\mathscr {A}, \mathscr {B}]_*=\mathscr {A}\mathscr {B}^*-\mathscr {B}\mathscr {A}^*$ ${[A, B]}_{*} = A B^{*} - B A^{*}$ are called a bi-skew Jordan and bi-skew Lie product, respectively. In this paper, it is shown that every non-additive mixed bi-skew Jordan and bi-skew Lie triple derivation $\Lambda : \mathcal {A}\rightarrow \mathcal {A}$ $Λ : A \to A$ is an additive $*$ $*$ -derivation.

Non-additive mixed bi-skew Jordan and bi-skew Lie triple derivations on \(*\)-algebras

摘要