Geodesic
Augmented down-up algebras and uniform posets
Ars Mathematica Contemporanea, Tome 6 (2013) no. 2, pp. 409-417.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

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.
DOI : 10.26493/1855-3974.508.23b
Keywords: Uniform poset, dual polar graph, dual polar space, down-up algebra 
@article{10_26493_1855_3974_508_23b,
     author = {Paul M. Terwilliger and Chalermpong Worawannotai},
     title = {Augmented down-up algebras and uniform posets},
     journal = {Ars Mathematica Contemporanea},
     pages = {409--417},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2013},
     doi = {10.26493/1855-3974.508.23b},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.508.23b/}
}
TY  - JOUR
AU  - Paul M. Terwilliger
AU  - Chalermpong Worawannotai
TI  - Augmented down-up algebras and uniform posets
JO  - Ars Mathematica Contemporanea
PY  - 2013
SP  - 409
EP  - 417
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.508.23b/
DO  - 10.26493/1855-3974.508.23b
LA  - en
ID  - 10_26493_1855_3974_508_23b
ER  - 
%0 Journal Article
%A Paul M. Terwilliger
%A Chalermpong Worawannotai
%T Augmented down-up algebras and uniform posets
%J Ars Mathematica Contemporanea
%D 2013
%P 409-417
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.508.23b/
%R 10.26493/1855-3974.508.23b
%G en
%F 10_26493_1855_3974_508_23b
Paul M. Terwilliger; Chalermpong Worawannotai. Augmented down-up algebras and uniform posets. Ars Mathematica Contemporanea, Tome 6 (2013) no. 2, pp. 409-417. doi : 10.26493/1855-3974.508.23b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.508.23b/

Cité par Sources :