Course details
Semester
- Spring 2023
- Monday, January 23rd to Friday, March 31st
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Thursdays
- 12:05 - 12:55 (UK)
Description
In the course, we will introduce the Yang-Baxter equation and the algebraic theory of skew braces. We will focus on radical rings as a concrete example of skew braces. We build the connection between set-theoretical solutions to the Yang-Baxter equation and skew braces: we show that any skew brace gives rise to a solution of the Yang-Baxter equation and that this construction is universal. We will finish the course by introducing fascinating connections among skew braces, regular subgroups and bijective 1-cocycles.
Prerequisites
- Essential: undergraduate group theory.
- Advantageous: undergraduate ring theory.
Syllabus
- The Yang-Baxter equation.
- Radical rings and set-theoretic solutions to the Yang-Baxter equation.
- Skew braces.
- Ideals.
- Skew braces and set-theoretic solutions to the Yang-Baxter equation.
- Skew braces and bijective 1-cocycles (optional).
- Skew braces and regular subgroups (optional).
Lecturer
-
Dr Ilaria Colazzo
- University
- University of Leeds
Bibliography
Follow the link for a book to take you to the relevant Google Book Search page
You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.
- A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation (Tatiana Gateva-Ivanova, arxiv) Download
- A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation (Tatiana Gateva-Ivanova, arxiv) Download
- Braces, radical rings, and the quantum Yang–Baxter equation (Wolfgang Rump, arxiv) Download
- Left Braces: Solutions of the Yang-Baxter Equation (Ferran Cedó, arxiv) Download
- Non-unitary set-theoretical solutions to the Quantum Yang-Baxter Equation (Alexandre Soloviev, arxiv) Download
- Problems on skew left braces (Leandro Vendramin, arxiv) Download
- Set-theoretical solutions to the quantum Yang-Baxter equation (Pavel Etingof, Travis Schedler and Alexandre Soloviev, arxiv) Download
- Skew braces and the Yang-Baxter equation (L. Guarnieri and L. Vendramin, arxiv) Download
Assessment
The assessment for this course will be released on Monday 1st May 2023 at 00:00 and is due in before Monday 15th May 2023 at 11:00.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
Only current consortium members and subscribers have access to these files.
Please log in to view course materials.
Lectures
Please log in to view lecture recordings.