The quantum algebra Uq(sl2) and its equitable presentation

@article{Ito2005TheQA,
  title={The quantum algebra Uq(sl2) and its equitable presentation},
  author={Tatsuro Ito and Paul M. Terwilliger and Chih-wen Weng},
  journal={Journal of Algebra},
  year={2005},
  volume={298},
  pages={284-301}
}
Leonard pairs associated with the equitable generators of the quantum algebra U q (sl 2)
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
The algebra Uq(sl2) in disguise
Linear Maps That Act Tridiagonally with Respect to Eigenbases of the Equitable Generators of Uq(sl2)
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
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)
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" ")"
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.
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