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Notions of equivalence among constant Yang--Baxter Operators: To -Equivalence and Beyond
Paul P. Martin, Eric C. Rowell
Recent advances in the classification of certain classes of Yang-Baxter operators through a holistic categorical approach has some of us wondering about ways to identify solutions.…
Paravortices: loop braid representations with both generators involutive
Paul P. Martin, Eric C. Rowell, Fiona Torzewska
We first motivate the study of a certain quotient of the loop braid category, both for the mathematics underpinning recent approaches to topological quantum computation; and as a k…
On Higher Representation Theory via Categories of type Charge-Conserving--with--Glue
Paul P Martin, Sarah Almateari, Eric C Rowell
In this paper we introduce a strict monoidal subcategory of the category of matrices, suitable to address a higher representation theoretic analogue of radicals (non-semisimplicity…
A Categorical Perspective on Braid Representations
P. P. Martin, E. C. Rowell, F. Torzewska
We study categories whose objects are the braid representations, that is, strict monoidal functors from the braid category to the category of matrices…
Solutions to the constant Yang-Baxter equation: additive charge conservation in three dimensions
Jarmo Hietarinta, Paul Martin, Eric C. Rowell
We find all solutions to the constant Yang--Baxter equation in three dimensions, subject to an additive charge-conservation ansatz. This ans…