Zobrazeno 1 - 10
of 183
pro vyhledávání: '"Rowell, Eric C."'
Given a premodular category $\mathcal{C}$, we show that its $R$-symbol can be recovered from its $T$-matrice, fusion coefficients and some 2nd generalized Frobenius-Schur indicators. In particular, if $\mathcal{C}$ is modular, its $R$-symbols for a c
Externí odkaz:
http://arxiv.org/abs/2408.02748
We construct all integral non-group-theoretical modular categories of dimension $p^2q^2$, where $p$ and $q$ are distinct prime numbers, establishing that a necessary and sufficient condition for their existence is that $p \mid q+1$, and their rank is
Externí odkaz:
http://arxiv.org/abs/2404.03826
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
Externí odkaz:
http://arxiv.org/abs/2311.17255
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 ansatz. This ansatz is a generalisation of (strict) charge-conservation, for which a c
Externí odkaz:
http://arxiv.org/abs/2310.03816
We use the computer algebraic system GAP to classify modular data up to rank 11, and integral modular data up to rank 12. This extends the previously obtained classification of modular data up to rank 6. Our classification includes all the modular da
Externí odkaz:
http://arxiv.org/abs/2308.09670
The construction and classification of super-modular categories is an ongoing project, of interest in algebra, topology and physics. In a recent paper, Cho, Kim, Seo and You produced two mysterious families of super-modular data, with no known realiz
Externí odkaz:
http://arxiv.org/abs/2305.09108
Here a loop braid representation is a monoidal functor $\mathsf{F}$ from the loop braid category $\mathsf{L}$ to a suitable target category, and is $N$-charge-conserving if that target is the category $\mathsf{Match}^N$ of charge-conserving matrices
Externí odkaz:
http://arxiv.org/abs/2301.13831
Autor:
Rowell, Eric C.
The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the mathematical stu
Externí odkaz:
http://arxiv.org/abs/2208.11762
Publikováno v:
Communications in Mathematical Physics (2023)
Modular data is the most significant invariant of a modular tensor category. We pursue an approach to the classification of modular data of modular tensor categories by building the modular $S$ and $T$ matrices directly from irreducible representatio
Externí odkaz:
http://arxiv.org/abs/2203.14829
Ocneanu rigidity implies that there are finitely many (braided) fusion categories with a given set of fusion rules. While there is no method for determining all such categories up to equivalence, there are a few cases for which can. For example, Kazh
Externí odkaz:
http://arxiv.org/abs/2202.00121