Classification of Spherical Fusion Categories of Frobenius–Schur Exponent 2

On the classification of certain fusion categories

We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories — and consequently, semisimple Hopf algebras — of dimension pq2, where p and q are distinct primes. This case is especially interesting because it is the simplest class of dimensions where not all integral fusion categories are group-theoretical. Secondly, we classify...

Eigenvalues of Rotations and Braids in Spherical Fusion Categories

We give formulas for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semi-simple spherical tensor category C. In particular, this implies for a finite depth planar algebra, the entire collection of rotation eigenvalues can be computed from the fusion rules and the traces of rotation at finitely many depths. If C is also...

Spherical 2-categories and 4-manifold Invariants

Fusion Categories Of

We classify semisimple rigid monoidal categories with two iso-morphism classes of simple objects over the field of complex numbers. In the appendix written by P. Etingof it is proved that the number of semisimple Hopf algebras with a given finite number of irreducible representations is finite.

the innovation of a statistical model to estimate dependable rainfall (dr) and develop it for determination and classification of drought and wet years of iran

آب حاصل از بارش منبع تأمین نیازهای بی شمار جانداران به ویژه انسان است و هرگونه کاهش در کم و کیف آن مستقیماً حیات موجودات زنده را تحت تأثیر منفی قرار می دهد. نوسان سال به سال بارش از ویژگی های اساسی و بسیار مهم بارش های سالانه ایران محسوب می شود که آثار زیان بار آن در تمام عرصه های اقتصادی، اجتماعی و حتی سیاسی- امنیتی به نحوی منعکس می شود. چون میزان آب ناشی از بارش یکی از مولفه های اصلی برنامه ...