Siu-Hung Ng

Classification of the Lie bialgebra structures on the Witt and Virasoro algebras

An automatic meter reading and control system for communicating with remote terminal points includes a central station which selectively communicates with a transponder controller unit at each terminal point via a plurality of distribution units, each serving several transponder controller units. The distribution controller units are responsive to various commands issued by the central station to selectively route the commands to specified transponder controller units to direct the transponder controller units to selectively carry out a load control operation, a meter reading operation or transfer of previously stored meter data from the transponder units to the central station in accordance with functions specified by the various commands.

Frobenius-Schur indicators and exponents of spherical categories

We obtain two formulae for the higher Frobenius?Schur indicators: one for a spherical fusion category in terms of the twist of its center and the other one for a modular tensor category in terms of its twist. The first one is a categorical generalization of an analogous result by Kashina, Sommerhauser, and Zhu for Hopf algebras, and the second one extends Bantays 2nd indicator formula for a conformal field theory to higher degrees. These formulae imply the sequence of higher indicators of an object in these categories is periodic. We define the notion of Frobenius?Schur (FS-)exponent of a pivotal category to be the global period of all these sequences of higher indicators, and we prove that the FS-exponent of a spherical fusion category is equal to the order of the twist of its center. Consequently, the FS-exponent of a spherical fusion category is a multiple of its exponent, in the sense of Etingof, by a factor not greater than 2. As applications of these results, we prove that the exponent and the dimension of a semisimple quasi-Hopf algebra H have the same prime divisors, which answers two questions of Etingof and Gelaki affirmatively for quasi-Hopf algebras. Moreover, we prove that the FS-exponent of H divides dim(H)4. In addition, if H is a group-theoretic quasi-Hopf algebra, the FS-exponent of H divides dim(H)2, and this upper bound is shown to be tight

Congruence Subgroups and Generalized Frobenius-Schur Indicators

We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category

Central invariants and higher indicators for semisimple quasi-Hopf algebras

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Hopf algebras of dimension pq, II

, an equivariant indicator of an object in

Congruence property in conformal field theory

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