| dc.date.accessioned | 2023-11-28T16:21:57Z | |
| dc.date.available | 2023-11-28T16:21:57Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://hdl.handle.net/10852/106007 | |
| dc.description.abstract | Operator algebras were born out of the attempt to give mathematically rigorous foundations to quantum mechanics, and its development has been higly influenced by the mathematical approaches to understanding quantum field theories. Symmetries, central characters in physics, are understood in these approaches as symmetries of operator algebras. With the changes of paradigms concerning symmetries in physics, there came changes of paradigms regarding the concept of symmetries of operator algebras.
This thesis elaborates on two main ideas: actions of quantum groups and C*-tensor categories. One can think of those as extensions to the category of noncommutative topological spaces of group theory and representation theory, respectively.
The topics we cover are: boundary actions, equivariant injectivity, Yetter-Drinfeld C*-algebras and factorization homology. | en_US |
| dc.language.iso | en | en_US |
| dc.relation.haspart | Paper I. Noncommutative Poisson boundaries and Furstenberg–Hamana boundaries of Drinfeld doubles. Erik Habbestad, Lucas Hataishi, Sergey Neshveyev. Published in Journal de Mathématiques Pures et Appliquées, March 2022, volume 159, issue 2, pp. 313-347. DOI: 10.1016/j.matpur.2021.12.006. The article is included in the thesis. Also available at: https://doi.org/10.1016/j.matpur.2021.12.006 | |
| dc.relation.haspart | Paper II. Injectivity for algebras and categories with quantum symmetry. Lucas Hataishi, Makoto Yamashita. To be published. The paper is not available in DUO awaiting publishing. Preprint at https://arxiv.org/abs/2205.06663 | |
| dc.relation.haspart | Paper III. Actions of compact and discrete quantum groups on operator systems. Joeri de Ro, Lucas Hataishi. To be published. The paper is not available in DUO awaiting publishing. Preprint at https://arxiv.org/abs/2304.14055 | |
| dc.relation.haspart | Paper IV. C∗-algebraic factorization homology and realization of cyclic representations. Lucas Hataishi. To be published. The paper is not available in DUO awaiting publishing. Preprint at https://arxiv.org/abs/2304.07155 | |
| dc.relation.uri | https://doi.org/10.1016/j.matpur.2021.12.006 | |
| dc.title | Quantum symmetries implemented by quantum groups and unitary tensor categories: Boundary theory, equivariant injective envelopes and factorization homology | en_US |
| dc.type | Doctoral thesis | en_US |
| dc.creator.author | Hataishi, Lucas Yudi | |
| dc.type.document | Doktoravhandling | en_US |