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

İsmet Altıntaş, Kemal Taskopru


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 $q=A^2$.


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

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