增广down-up代数与一致偏序集
Augmented down-up algebras and uniform posets
摘要：
受一致偏序集结构的启发，我们引入了增广下上（或ADU）代数的概念。讨论了ADU代数与Benkart和Roby定义的down-up代数之间的关系。对于每一个ADU代数，我们给出了生成元和关系的两种表示。我们还显示了一个$Z$分级和线性基础。此外，我们还证明了中心同构于一个二元多项式代数。我们展示了七个家庭的一致偏序集，并表明，每个给一个ADU代数模在一个自然的方式。ADU代数概念的主要灵感来自于第二作者的论文，该论文涉及使用对偶极图构造的一类一致偏序集。
英文摘要：
Motivated by the structure of the uniform posets we introduce the notion of an augmented down-up (or ADU) algebra. We discuss how ADU algebras are related to the down-up algebras defined by Benkart and Roby. For each ADU algebra we give two presentations by generators and relations. We also display a $Z$-grading and a linear basis. In addition we show that the center is isomorphic to a polynomial algebra in two variables. We display seven families of uniform posets and show that each gives an ADU algebra module in a natural way. The main inspiration for the ADU algebra concept comes from the second author's thesis concerning a type of uniform poset constructed using a dual polar graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
