Zobrazeno 1 - 10
of 915
pro vyhledávání: '"DELANEY, COLLEEN"'
We introduce the condensed fiber product of two $G$-crossed braided fusion categories, generalizing existing constructions in the literature. We show that this product is closely related to the cohomological construction known as zesting. Furthermore
Externí odkaz:
http://arxiv.org/abs/2410.09025
We study the boundaries of the positroid cells which arise from N = 4 super Yang Mills theory. Our main tool is a new diagrammatic object which generalizes the Wilson loop diagrams used to represent interactions in the theory. We prove conditions und
Externí odkaz:
http://arxiv.org/abs/2401.05592
Quantum topology provides various frameworks for defining and computing invariants of manifolds inspired by quantum theory. One such framework of substantial interest in both mathematics and physics is the Turaev-Viro-Barrett-Westbury state sum const
Externí odkaz:
http://arxiv.org/abs/2311.08514
For a finite group $G$, a $G$-crossed braided fusion category is $G$-graded fusion category with additional structures, namely a $G$-action and a $G$-braiding. We develop the notion of $G$-crossed braided zesting: an explicit method for constructing
Externí odkaz:
http://arxiv.org/abs/2212.05336
Autor:
Liu, Winnie L., Kampouri, Eleftheria, Bui, John K., Sekhon, Mandeep K., Tercero, Almudena, Finlay, Dan, Asghedom, Liya H., Romasanta, Gladys R., Rice, Natalie T., Ranjbaran, Fatima, Stoltzman, Carrie, Cook, Jody, Blake, Joe, Delaney, Colleen S., Hill, Joshua A.
Publikováno v:
In Molecular Therapy - Methods & Clinical Development 12 December 2024 32(4)
We show that the ribbon zesting construction can produce modular isotopes -- different modular fusion categories with the same modular data. The result relies on the observation that the Reshetikhin-Turaev invariants of framed links associated to a r
Externí odkaz:
http://arxiv.org/abs/2107.11374
We give a rigorous development of the construction of new braided fusion categories from a given category known as zesting. This method has been used in the past to provide categorifications of new fusion rule algebras, modular data, and minimal modu
Externí odkaz:
http://arxiv.org/abs/2005.05544
Autor:
Delaney, Colleen
We give a construction and algorithmic description of the fusion ring of permutation extensions of an arbitrary modular tensor category using a combinatorial approach inspired by the physics of anyons and symmetry defects in bosonic topological phase
Externí odkaz:
http://arxiv.org/abs/1909.03003
Autor:
Delaney, Colleen, Wang, Zhenghan
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions of unitary
Externí odkaz:
http://arxiv.org/abs/1811.02143
Autor:
Delaney, Colleen, Tran, Alan
The smallest known example of a family of modular categories that is not determined by its modular data are the rank 49 categories $\mathcal{Z}(\text{Vec}_G^{\omega})$ for $G=\mathbb{Z}_{11} \rtimes \mathbb{Z}_{5}$. However, these categories can be d
Externí odkaz:
http://arxiv.org/abs/1806.02843