Quantum groups and the Yang-Baxter equation

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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.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2016
Issuance monographic
Language English


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-


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

© 2016 by Valentin Buciumas
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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