20.500.12556/RUL-148248 Kvantne vozelne invariante delo diplomskega seminarja Quantum knot invariants V tem delu bomo definirali pentljaste Hopfove algebre in $rv$-vozle. S pomočjo le teh bomo vpeljali kvantne vozlene invariante in s pomočjo kvantne \(\mathfrak{sl}_2\) izračunali Jonesov polinom deteljice. Ta formulacija kvantnih vozelnih invariant sledi pristopu R. v.d. Veena [Introduction to quantum invariants of knots] in D. Bar-Natana [Universal tangle invariants and docile perturbed Gaussians]. In this thesis, we are going to define ribbon Hopf algebras and $rv$-knots. Building on these definitions, we are going to introduce quantum knot invariants. In the end, we are going to compute the Jones polynomial of the trefoil with the help of quantum $\mathfrak{sl}_2$. This formulation of quantum invariants follows that of R. van der Veen [Introduction to quantum invariants of knots] and D. Bar-Natana [Universal tangle invariants and docile perturbed Gaussians]. Kvazi-trikotna Hopfova algebra pentljasta Hopfova algebra rv-vozel kvantna vozelna invarianta Jonesov polinom Quasi-triangular Hopf algebra ribbon Hopf algebra rv-knot quantum knot invariant Jones polynomial true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-08-05 08:15:12 2023-08-05 08:15:16 2024-05-29 10:44:25 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 134318 161920771 8015.pdf 8015.pdf 1 0E881FE4B62F0E24FF1C7D96904369CC dfa1ef493a020a8200ce57d098167a5504e8e33a4d5ff40eaf9b36a28cae7861 58141342-3357-11ee-aeaf-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=172303 Fakulteta za matematiko in fiziko 0 0 0