Irreducible Representations of Jordanian Quantum Algebra ${\cal U}_h(sl(2))$ Via a Nonlinear Map

B. Abdesselam; A. Chakrabarti; R. Chakrabarti

doi:10.1142/S0217732396002861

Irreducible Representations of Jordanian Quantum Algebra ${\cal U}_h(sl(2))$ Via a Nonlinear Map

q-alg 2009-10-30 v6 Quantum Algebra

Authors: B. Abdesselam , A. Chakrabarti , R. Chakrabarti

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Abstract

The generators of the Jordanian quantum algebra ${\cal U}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction of the finite dimensional irreducible representations of the algebra ${\cal U}_h(sl(2))$ . Using this construction, new finite dimensional solutions of the Yang-Baxter equation may be obtained.

Keywords

Jordanian quantum algebra irreducible representations nonlinear map Yang-Baxter equation sl(2)

Cite

@article{arxiv.q-alg/9606014,
  title  = {Irreducible Representations of Jordanian Quantum Algebra ${\cal U}_h(sl(2))$ Via a Nonlinear Map},
  author = {B. Abdesselam and A. Chakrabarti and R. Chakrabarti},
  journal= {arXiv preprint arXiv:q-alg/9606014},
  year   = {2009}
}

Comments

10 pages, latex-file, references and some comments are added, version to be published in Mod. Phys. Lett

Irreducible Representations of Jordanian Quantum Algebra ${\cal U}_h(sl(2))$ Via a Nonlinear Map

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