Ideal Structure of the Kauffman and Related Monoids
Ideal Structure of the Kauffman and Related Monoids
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DOI：
10.1080/00927870600651414
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发表时间：
2006-08
影响因子：
0.7
通讯作者：
K. Lau;D. Fitzgerald
中科院分区：
文献类型：
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作者：
K. Lau;D. Fitzgerald
Temperley-Lieb 代数的生成器生成具有吸引人的几何表示的幺半群。人们对此进行了大量研究，尤其是路易斯·考夫曼。 Borisavljević、Došen 和 Petrić 完整地证明了生成元和关系式的抽象表示，并建议将其命名为“考夫曼幺半群”。我们将半群理论引入到考夫曼幺半群的某个有限同态图像的研究中。我们将同态图像（琼斯幺半群）展示为具有线性有序理想的组合和正则 *-半群。考夫曼幺半群是用琼斯幺半群和纯组合数值函数明确描述的。我们用它来描述考夫曼幺半群及其另外两个同态图像的理想结构。
The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljević, Došen, and Petrić gave a complete proof of its abstract presentation by generators and relations, and suggested the name “Kauffman monoid”. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid and two other of its homomorphic images.