Some Calculations on Link Polynomials from 2-Parameter Quantum Groups |
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| Institution: | 1. Department of mathematical sciences, College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia;2. Department of Nutrition, Cihan University-Erbil, Kurdistan Region, Iraq;3. Mathematics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia;4. Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, KSA, Makkah, Saudi Arabia;5. Mathematics Department, Faculty of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia;6. Physics Department, College of Science, Al-Zulfi, Majmaah University, AL-Majmaah 11952, Saudi Arabia;1. Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, 212013, China;2. Department of Mathematics, Obour High Institute For Engineering and Technology, Cairo, 11828, Egypt;3. Department of Mathematics, Faculty of Science, Taif University, Taif, P. O. Box 11099 PLXOP21944, Saudi Arabia;4. School of Management & Economics, Jiangsu University of Science and Technology, Zhenjiang 212003, China;5. Department of Basic Science, Higher Technological Institute, 44634 10th of Ramadan City, Egypt |
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| Abstract: | Starting with the link invariant G (p,q,z) , a skein relation is introduced which enables us to calculate the polynomial starting with G (p,q,z) = 1, for the unknot. The relation between G (p,q,z) and the known 2-variable link invariant K (l,m) is shown. Then the polynomial of some common knots is calculated, also it is shown that this invariant failed to distinguish the Birmans pairs as well as Jones invariant. |
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