由两组相互正交的幂等元生成的代数
An algebra generated by two sets of mutually orthogonal idempotents
摘要：
对于域$F$和整数$d\geq 1$，我们考虑由两组$d+1$相互正交的幂等元生成的泛结合$F$ -代数$A$.我们显示四个基地的$F$向量空间$A$，我们发现有吸引力的。我们确定这些碱基是如何相互关联的。我们描述如何在$A$乘法看起来相对于我们的基地。利用我们的基，我们得到了$A$的一个无限嵌套的双边理想序列。利用我们的基，我们得到了一个涉及某个$F$ -线性映射$\partial: A \to A$的无穷正合序列.我们得到几个结果的核心$\partial$，例如，这个核心是一个子代数的$A$是免费的秩$d$。
英文摘要：
For a field $F$ and an integer $d\geq 1$, we consider the universal associative $F$-algebra $A$ generated by two sets of $d+1$ mutually orthogonal idempotents. We display four bases for the $F$-vector space $A$ that we find attractive. We determine how these bases are related to each other. We describe how the multiplication in $A$ looks with respect to our bases. Using our bases we obtain an infinite nested sequence of 2-sided ideals for $A$. Using our bases we obtain an infinite exact sequence involving a certain $F$-linear map $\partial: A \to A$. We obtain several results concerning the kernel of $\partial$; for instance this kernel is a subalgebra of $A$ that is free of rank $d$.
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