Nonassociative algebraic structures

• Thesis title in Czech: Neasociativní algebraické struktury
• Thesis title in English: Nonassociative algebraic structures
• Academic year of topic announcement: 2021/2022
• Thesis type: dissertation
• Thesis language: angličtina
• Department: Department of Algebra (32-KA)
• Supervisor: doc. RNDr. David Stanovský, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 22.09.2021
• Date of assignment: 22.09.2021
• Confirmed by Study dept. on: 22.09.2021

Guidelines

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.

References

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.