非表示代数的不可约表示的构造
Constructing irreducible representations of finitely presented algebras
摘要：
通过结合非交换代数和计算交换代数的著名技术，我们观察到一种算法方法可以应用于研究非交换代数的不可约表示。更详细地说：假设$n$是正整数，$k$是可计算域，$\bar{k}$表示$k$的代数闭包，而$M_n(\bar{k})$表示元素在$\bar{k}$中的$n \times n$矩阵的代数。设$R$是表示的$k$ -代数.在$k$上计算，该过程将（a）决定是否存在不可约表示$R \to M_n(\bar{k})$，以及（b）如果至少存在一个不可约表示，则显式地构造不可约表示$R \to M_n(\bar{k})$。(For（b），有必要假设$k[x]$配备有因子分解算法。）通过一个基本的例子。
英文摘要：
By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In slightly more detail: Assume that $n$ is a positive integer, that $k$ is a computable field, that $\bar{k}$ denotes the algebraic closure of $k$, and that $M_n(\bar{k})$ denotes the algebra of $n \times n$ matrices with entries in $\bar{k}$. Let $R$ be a finitely presented $k$-algebra. Calculating over $k$, the procedure will (a) decide whether an irreducible representation $R \to M_n(\bar{k})$ exists, and (b) explicitly construct an irreducible representation $R \to M_n(\bar{k})$ if at least one exists. (For (b), it is necessary to assume that $k[x]$ is equipped with a factoring algorithm.) An elementary example is worked through.
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