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  1. ; ; (, Communications in Mathematical Physics)
    Abstract Zesting of braided fusion categories is a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. In this paper, we classify and construct all possible braided zesting data for modular categories associated with quantum groups at roots of unity. We produce closed formulas, based on the root system of the associated Lie algebra, for the modular data of these new modular categories. 
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  2. ; ; ; ; (, Journal of the London Mathematical Society)
    Abstract For a finite group , a ‐crossed braided fusion category is a ‐graded fusion category with additional structures, namely, a ‐action and a ‐braiding. We develop the notion of ‐crossed braided zesting: an explicit method for constructing new ‐crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group . This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All ‐crossed braided zestings of a given category are ‐extensions of their trivial component and can be interpreted in terms of the homotopy‐based description of Etingof, Nikshych, and Ostrik. In particular, we explicitly describe which ‐extensions correspond to ‐crossed braided zestings. 
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  3. ; ; (, American Math Society)
    Free, publicly-accessible full text available June 18, 2026
  4. ; ; (, Journal of Algebra)
    Free, publicly-accessible full text available March 1, 2026
  5. ; ; (, Bulletin of the Belgian Mathematical Society - Simon Stevin)
    Free, publicly-accessible full text available November 16, 2025
  6. ; ; (, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)
    We find all solutions to the constant Yang–Baxter equation R 12 R 13 R 23 = R 23 R 13 R 12 in three dimensions, subject to an additive charge-conservation (ACC) ansatz. This ansatz is a generalization of (strict) charge-conservation, for which a complete classification in all dimensions was recently obtained. ACC introduces additional sector-coupling parameters—in three dimensions, there are four such parameters. In the generic dimension 3 case, in which all of the four parameters are non-zero, we find there is a single three parameter family of solutions. We give a complete analysis of this solution, giving the structure of the centralizer (symmetry) algebra in all orders. We also solve the remaining cases with three, two or one non-zero sector-coupling parameter(s). 
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  7. ; ; (, Journal of Algebra)
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  8. ; ; ; (, Communications in Mathematical Physics)
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