The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$

Details The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$ The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$

2011-07-18

arxiv.org/abs/1107.3544v3

SIGMA 7 (2011), 099, 26 pages

Mathematics

Quantum Algebra

misprint in Lemma 7.1 is corrected

Scientific paper

10.3842/SIGMA.2011.099

Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $\Delta$ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between $\Delta$ and the quantum algebra $U_q(\mathfrak{sl}_2)$. Our main result is an algebra injection from $\Delta$ into a relative of $U_q(\mathfrak{sl}_2)$; the relative is obtained from $U_q(\mathfrak{sl}_2)$ by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of $U_q(\mathfrak{sl}_2)$

Affiliated with

Also associated with

No associations

Rating

The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$ 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 and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\mathfrak{sl}_2)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-272568