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arXiv · 1206.0455

Augmented down-up algebras and uniform posets

Paul Terwilliger·Chalermpong Worawannotai
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Abstract

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.

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Paul Terwilliger, Chalermpong Worawannotai. 2012-06-03. Augmented down-up algebras and uniform posets. https://arxiv.org/abs/1206.0455

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