Polynomial \(G_L\), Yang-Baxter Equation and Quantum Group \(SL(2)_q\) - Altıntaş, ć°smet; Taskopru, Kemal (Communications in Mathematics and Applications, 2016)
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 $q=A^2$.