## 81 Citations

The equitable presentation for the quantum group Uq(g) associated with a symmetrizable Kac–Moody algebra g

- Mathematics
- 2005

Leonard pairs associated with the equitable generators of the quantum algebra U q (sl 2)

- Mathematics
- 2011

Let ℱ denote an algebraically closed field, and fix a nonzero q ∈ ℱ that is not a root of unity. Consider the quantum algebra U q (sl 2) over ℱ with equitable generators X ±1, Y and Z. In the first…

Dual polar graphs, the quantum algebra U_q(sl_2), and Leonard systems of dual q-Krawtchouk type

- Mathematics
- 2012

Linear Maps That Act Tridiagonally with Respect to Eigenbases of the Equitable Generators of Uq(sl2)

- Mathematics
- 2020

Let F denote an algebraically closed field; let q be a nonzero scalar in F such that q is not a root of unity; let d be a nonnegative integer; and let X, Y, Z be the equitable generators of Uq(sl2)…

TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS

- Mathematics
- 2005

Let 𝕂 denote an algebraically closed field with characteristic 0, and let q denote a nonzero scalar in 𝕂 that is not a root of unity. Let 𝔸q denote the unital associative 𝕂-algebra defined by…

The equitable presentation for the quantum group νq(sl2)

- MathematicsJournal of Mathematical Physics
- 2019

We introduce a new Hopf algebra Aq(sl2), consider the equitable presentation of the quantum group νq(sl2), and prove that the algebra νq(sl(2)) is a homomorphic image of Aq(sl2). We also give some…

Leonard Pairs from the Equitable Generators of "U" _"q" "(" 〖"sl" 〗_"2" ")"

- Mathematics
- 2011

Let F denote an algebraically closed field and fix a nonzero q∈F that is not a root of unity. Consider the quantum algebra U_q (sl_2) over F with equitable generators x^(±1),y and z. Let A (resp.…

## References

SHOWING 1-10 OF 79 REFERENCES

The equitable presentation for the quantum group Uq(g) associated with a symmetrizable Kac–Moody algebra g

- Mathematics
- 2005

Tridiagonal pairs and the quantum affine algebra Uq(sl2) (代数的組合せ論)

- Mathematics
- 2005

Let K denote an algebraically closed field and let q denote a nonzero scalar in K that is not a root of unity. Let V denote a vector space over K with finite positive dimension and let A, A∗ denote a…

Representations of the cyclically symmetric q-deformed algebra soq(3)

- Mathematics
- 1998

An algebra homomorphism ψ from the nonstandard q-deformed (cyclically symmetric) algebra Uq(so3) to the extension Uq(sl2) of the Hopf algebra Uq(sl2) is constructed. Not all irreducible…

Representation theory and q-boson realizations of Witten's su(2) and su(1, 1) deformations

- Mathematics
- 1993

A Class of Algebras Similar to the Enveloping Algebra of sl(2)

- Mathematics
- 1990

Fix f E C[X]. Define R = C[A, B, H] subject to the relations HA-AH = A, HB-BH =-B, AB-BA = f(H). We study these algebras (for different f) and in particular show how they are similar to (and…

Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

A class of algebras similar to the enveloping algebra of (2)

- Mathematics
- 1990

Fix f E C[X]. Define R = C[A, B, H] subject to the relations HA-AH = A, HB-BH =-B, AB-BA = f(H). We study these algebras (for different f) and in particular show how they are similar to (and…

“Hidden symmetry” of Askey-Wilson polynomials

- Mathematics
- 1991

ConclusionsWe have shown that the Askey-Wilson polynomials of general form are generated by the algebra AW(3), which has a fairly simple structure and is the q-analog of a Lie algebra with three…