0 KB310 KB19 KB200820252013Terwilliger, PaulWorawannotai, Chalermpongštevilka:2letnik:6str. 409-417COBISSID:16790873ISSN:1855-3966URN:URN:NBN:SI:doc-YVKX9XUCenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneadown-up algebradual polar graphdual polar spaceuniform posetAugmented down-up algebras and uniform posets|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 graphMotivirani s strukturo uniformnih delno urejenih množic definiramo tako imenovano razširjeno downup algebro (augmented down-up algebra ali na kratko ADU). Razložimo, kako je ADU algebra povezana z down-up algebro, ki sta jo definirala Benkart in Roby. Za vsako ADU algebro podamo dve prezentaciji z generatorji in relacijami. Razložimo tudi ?$\mathbb{Z}$?-grading in linearno bazo. Poleg tega pokažemo, da je center ADU algebre izomorfen algebri polinomov dveh spremenljivk. Podamo sedem družin uniformnih delno urejenih množic in pokažemo, da vsaka naravno porodi modul ADU algebre. Glavna inspiracija za študij ADU algebre prihaja iz doktorske disertacije drugega avtorjaTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije