左輸帶的特徵值之研究

Abstract

左輸帶是半群的一種特例，本篇論文介紹左輸帶的定義並給兩個重要的例 子。如對左輸帶內的元素給定機率分佈，可由其隨機漫步得到轉移矩陣，其特徵 值與重數的性質探討為本論文之重點，我們介紹一個已知結果並對照我們所做的 例子。

A left regular band (LRB) is a semigroup. We will give the definition and examples of LRBs. The transition matrix is defined from running random walks on an LRB with a given probability distribution. For a theorem of Brown, the eigenvalues of such a transition matrix are completely determined. We will check the theorem with our examples.