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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…
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…