Polynomial \(G_L\), Yang-Baxter Equation and Quantum Group \(SL(2)_q\)

Authors

  • ć°smet Altıntaş Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, 54187
  • Kemal Taskopru Department of Mathematics, Faculty of Arts and Sciences, Bilecik Seyh Edebali University, Bilecik, 11000

DOI:

https://doi.org/10.26713/cma.v7i1.382

Keywords:

Polynomial \(G_L\), Jones polynomial, Regular isotopy, Braid, Abstract tensor, Vacuum-vacuum expectation, Quantum group \(SL(2)_q\)

Abstract

In this paper, we define the polynomial \(G_L\) by way of the braids. We construct the abstract tensor model of the polynomial \(G_L\) and we obtain the new solutions relevant with the state model of the polynomial \(G_L\) to the Yang-Baxter equation. We also construct the vacuum-vacuum expectation model of the polynomial \(G_L\) and we show that the studies performed using the Kaufmann bracket on the quantum group \(SL(2)_q\) with \(q = A^2\) are valid for the state model of the polynomial \(G_L\) without $q=A^2$.

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References

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Published

15-06-2016
CITATION

How to Cite

Altıntaş, ć°smet, & Taskopru, K. (2016). Polynomial \(G_L\), Yang-Baxter Equation and Quantum Group \(SL(2)_q\). Communications in Mathematics and Applications, 7(1), 55–72. https://doi.org/10.26713/cma.v7i1.382

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Section

Research Article