Quantum groups and the Yang-Baxter equation
Abstract/Contents
- Abstract
- In this thesis we will present a series of reconstruction results for Hopf algebras due to Saavedra-Rivano, Majid and Ulbrich. We will then apply them to solutions of the non-parametrized Yang-Baxter equation and recover the FRT construction, due to Faddeev, Reshetikhin and Takhtajan. The novel part is the application of the reconstruction theorem to a parametrized solution of the Yang-Baxter equation to develop a parametrized FRT construction. We apply this construction to the parametrized solution of the Yang-Baxter equation corresponding to the quantum group $U_q(\widehat{\mathfrak{sl}_2})$ and to another solution with parameter group $GL(2, \mathbb{C}) \times GL(1, \mathbb{C})$ that doesn't come from any known quantum group and build two new quantum groups. We study the representation theory of the newly built objects.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Buciumas, Valentin |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Bump, Daniel, 1952- |
| Thesis advisor | Bump, Daniel, 1952- |
| Thesis advisor | Venkatesh, Akshay, 1981- |
| Thesis advisor | Yun, Zhiwei, 1982- |
| Advisor | Venkatesh, Akshay, 1981- |
| Advisor | Yun, Zhiwei, 1982- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Valentin Buciumas. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Valentin Buciumas
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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