论文标题
关于$ p \ times q $矩阵的约旦三重系统的不可还原表示
On the irreducible representations of the Jordan triple system of $p \times q$ matrices
论文作者
论文摘要
令$ \ Mathcal {J} _ {\ field} $为所有$ p \ times q $的约旦三重系统（$ p \ neq q $; $ p，q> 1）$矩形矩阵field $ \ field $ \ field $ field themativical 0具有特征性0，带有Triple Product $ y $的转置。我们研究$ \ Mathcal {j} $ of $ \ Mathcal {J} _ {\ field} $的通用联络$ \ MATHCAL {U}（\ MATHCAL {J} _ {\ field}）$ p+q}（\ field）$，其中$ m_ {p+q \ times p+q}（\ field）$是所有$（p+q）\ times \ times（p+q）$矩阵上$ \ field $的普通关联代数。因此，仅存在$ \ Mathcal {J} _ {\ field} $的一个非平凡的不可约表示。推导$ \ Mathcal {U}（\ Mathcal {J} _ {\ field}）$的中心。
Let $\mathcal{J}_{\field}$ be the Jordan triple system of all $p \times q$ ($p\neq q$; $p,q >1)$ rectangular matrices over a field $\field$ of characteristic 0 with the triple product $\{x,y,z\}= x y^t z+ z y^t x $, where $y^t$ is the transpose of $y$. We study the universal associative envelope $\mathcal{U}(\mathcal{J}_{\field})$ of $\mathcal{J}_{\field}$ and show that $\mathcal{U}(\mathcal{J}_{\field}) \cong M_{p+q \times p+q}(\field)$, where $M_{p+q\times p+q} (\field)$ is the ordinary associative algebra of all $(p+q) \times (p+q)$ matrices over $\field$. It follows that there exist only one nontrivial irreducible representation of $\mathcal{J}_{\field}$. The center of $\mathcal{U}(\mathcal{J}_{\field})$ is deduced.
