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 ?$\mathbb{Z}$?-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 authors thesis concerning a type of uniform poset constructed using a dual polar graph.

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URN

URN:NBN:SI:doc-YVKX9XUC

COBISSID

16790873

Added

16.12.2021

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Citation

APA:

Terwilliger, Paul, Worawannotai, Chalermpong (2013). Augmented down-up algebras and uniform posets. Ars mathematica contemporanea, volume 6, issue 2, str. 409-417. URN:NBN:SI:doc-YVKX9XUC from http://www.dlib.si

MLA:

Terwilliger, Paul, Worawannotai, Chalermpong. "Augmented down-up algebras and uniform posets." Ars mathematica contemporanea volume 6. issue 2 (2013) str. 409-417.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-YVKX9XUC>

Ars mathematica contemporanea
2008-
(Assembly record)