Nonassociative algebraic structures
| Název práce v češtině: | Neasociativní algebraické struktury |
|---|---|
| Název v anglickém jazyce: | Nonassociative algebraic structures |
| Klíčová slova: | rack|quandle|knot|link|non-associative structure|universal algebra|group theory|core|conjugation|coloring|Shannon entropy|Hayashi conjecture|homogeneous|connected|Latin|faithful. |
| Klíčová slova anglicky: | rack|quandle|knot|link|non-associative structure|universal algebra|group theory|core|conjugation|coloring|Shannon entropy|Hayashi conjecture|homogeneous|connected|Latin|faithful. |
| Akademický rok vypsání: | 2021/2022 |
| Typ práce: | disertační práce |
| Jazyk práce: | angličtina |
| Ústav: | Katedra algebry (32-KA) |
| Vedoucí / školitel: | doc. RNDr. David Stanovský, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 22.09.2021 |
| Datum zadání: | 22.09.2021 |
| Datum potvrzení stud. oddělením: | 22.09.2021 |
| Datum odevzdání elektronické podoby: | 06.06.2025 |
| Datum odevzdání tištěné podoby: | 10.06.2025 |
| Oponenti: | |
| Mgr. Petr Vojtěchovský, Ph.D. | |
| Zásady pro vypracování |
| The subject of the thesis will be various classes of algebraic structures related to knot theory and the quantum Yang-Baxter equation. This includes various types of self-distributivite structures, such as racks and quandles. We may also focus on other types of set-theoretic solutions of QYBE, including biquandles and braces. The aim is to develop a structure theory or classification for selected classes, or their applications in the respective fields. The main tools will come from group theory and universal algebra. |
| Seznam odborné literatury |
| M. Elhamdadi, S. Nelson, Quandles: an introduction to the algebra of knots. Student Mathematical Library, 74. American Mathematical Society, Providence, RI, 2015.
N. Andruskiewitsch, M. Graňa, From racks to pointed Hopf algebras. Adv. Math. 178 (2003), no. 2, 177-243. P. Etingof, T. Schedler, and A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209. A. Hulpke, D. Stanovský, P. Vojtěchovský, Connected quandles and transitive groups, J. Pure Appl. Algebra 220/2 (2016) 735--758. D. Stanovský, P. Vojtěchovský, Idempotent solutions of the Yang-Baxter equation and twisted Ward quasigroups, to appear in Fundamenta Math. |