Kvantne vozelne invariante : delo diplomskega seminarja

Grlj, Jernej (avtor), Strle, Sašo (mentor)

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].

• Jezik: Slovenski jezik
• Ključne besede: Kvazi-trikotna Hopfova algebra, pentljasta Hopfova algebra, rv-vozel, kvantna vozelna invarianta, Jonesov polinom
• Vrsta gradiva: Delo diplomskega seminarja/zaključno seminarsko delo/naloga
• Tipologija: 2.11 - Diplomsko delo
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2023
• PID: 20.500.12556/RUL-148248
• UDK: 515.1
• COBISS.SI-ID: 161920771
• Datum objave v RUL: 05.08.2023

Sekundarni jezik

• Jezik: Angleški jezik
• Naslov: Quantum knot invariants

Izvleček

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].

• Ključne besede: Quasi-triangular Hopf algebra, ribbon Hopf algebra, rv-knot, quantum knot invariant, Jones polynomial