The Universal Askey-Wilson Algebra

Details The Universal Askey-Wilson Algebra The Universal Askey-Wilson Algebra

2011-04-14

arxiv.org/abs/1104.2813v2

SIGMA 7 (2011), 069

Mathematics

Rings and Algebras

24 pages

Scientific paper

10.3842/SIGMA.2011.069

In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension $\Delta$ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call $\Delta$ the {\it universal Askey-Wilson algebra}. We give a faithful action of the modular group ${\rm {PSL}}_2({\mathbb Z})$ on $\Delta$ as a group of automorphisms. We give a linear basis for $\Delta$. We describe the center of $\Delta$ and the 2-sided ideal $\Delta[\Delta,\Delta]\Delta$. We discuss how $\Delta$ is related to the $q$-Onsager algebra.

Affiliated with

Also associated with

No associations

Rating

The Universal Askey-Wilson Algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Universal Askey-Wilson Algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Universal Askey-Wilson Algebra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-167031