On the Classification of Non-self-dual Modular Categories
نویسندگان
چکیده
We classify pseudo-unitary modular categories of rank at most 5 under the assumption that some simple object is not isomorphic to its dual. Our approach uses Gröbner basis computations, and suggests a general computational procedure for classifying low-rank modular categories.
منابع مشابه
On the Classification of the Grothendieck Rings of Non-self-dual Modular Categories
We develop a symbolic computational approach to classifying lowrank modular fusion categories, up to finite ambiguity. By a generalized form of Ocneanu rigidity due to Etingof, Ostrik and Nikshych, it is enough to classify modular fusion algebras of a given rank–that is, to determine the possible Grothendieck rings with modular realizations. We use this technique to classify modular categories ...
متن کاملFinitely semisimple spherical categories and modular categories are self - dual
We show that every essentially small finitely semisimple k-linear additive spherical category in which k = End(1) is a field, is equivalent to its dual over the long canonical forgetful functor. This includes the special case of modular categories. In order to prove this result, we show that the universal coend of the spherical category with respect to the long forgetful functor is self-dual as...
متن کاملFixed point theorem for non-self mappings and its applications in the modular space
In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...
متن کاملModular Categories, Integrality and Egyptian Fractions
It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank n. This follows from a double-exponential bound on the maximal denominator in an Egyptian fraction representation of 1. A näıve computer search approach to the classification of rank n integral modular categories using this bound quickly overwhelms th...
متن کاملOn duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009