论文标题
在三角代数上撒谎
Lie Biderivations on Triangular Algebras
论文作者
论文摘要
令$ \ Mathcal {t} $为交换环$ \ Mathcal {r} $和$φ：\ Mathcal {t} \ times \ times \ Mathcal {t} \ LongrightArrow \ Mathcal \ Mathcal {t} $是$ biderivation $ bidcal，我们将解决当前工作中描述$φ$形式的问题。结果表明，在某些温和的假设下，$φ$是内部biderivation和极端biderivation和一些中央双线性映射的总和。我们的结果立即应用于阻止上三角代数和希尔伯特太空巢代数。
Let $\mathcal{T}$ be a triangular algebra over a commutative ring $\mathcal{R}$ and $φ: \mathcal{T} \times \mathcal{T}\longrightarrow \mathcal{T}$ be an arbitrary Lie biderivation of $\mathcal{T}$. We will address the question of describing the form of $φ$ in the current work. It is shown that under certain mild assumptions, $φ$ is the sum of an inner biderivation and an extremal biderivation and a some central bilinear mapping. Our results is immediately applied to block upper triangular algebras and Hilbert space nest algebras .
