Quasi Three-parametric \(R\)-matrix and Quantum Supergroups \(GL_{p,q}(1/1)\) and \(U_{p,q}[\textit{gl}(1/1)]\)

Nguyen Thi Hong Van, Nguyen Anh Ky
Author affiliations

Authors

  • Nguyen Thi Hong Van Institute of Physics, VAST
  • Nguyen Anh Ky Institute of Physics, VAST

DOI:

https://doi.org/10.15625/0868-3166/29/4/14009

Keywords:

Quantum supergroup, R-matrix, Drinfel'd-Jimbo deformation, Multi- parametric quantum deformation

Abstract

An overparametrized (three-parametric) R-matrix satisfying a graded Yang-Baxter equation is introduced. It turns out that such an overparametrization is very helpful. Indeed, this R-matrix with one of the parameters being auxiliary, thus, reducible to a two-parametric R-matrix, allows the construction of quantum supergroups GLp,q(1/1) and Up,q[gl(1/1)] which, respectively, are two-parametric deformations of the supergroup GL(1/1) and the universal enveloping algebra U[gl(1/1)]. These two-parametric quantum deformations GLpq(1/1) and Upq[gl(1/1)], to our knowledge, are constructed for the first time via the present approach. The quantum deformation Up,q[gl(1/1)] obtained here is a true two-parametric deformation of Drinfel’d-Jimbo’s type, unlike some other one obtained previously elsewhere.

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Published

16-12-2019

How to Cite

[1]
N. T. H. Van and N. Anh Ky, “Quasi Three-parametric \(R\)-matrix and Quantum Supergroups \(GL_{p,q}(1/1)\) and \(U_{p,q}[\textit{gl}(1/1)]\)”, Comm. Phys., vol. 29, no. 4, p. 511, Dec. 2019.

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Papers
Received 23-07-2019
Accepted 05-11-2019
Published 16-12-2019