Classically, the exponent of a group is the least common multiple of the orders of its elements. This notion was generalized by Etingof and Gelaki to the context of Hopf algebras. Kashina, Sommerhäuser and Zhu later observed that there is a strong connection between exponents and Frobenius– Schur indicators. In this paper, we introduce the notion of twisted exponents and show that there is a si...

We present and analyze a gedanken experiment and show that the assumption that an antenna operating at a single frequency can transmit more than two independent information channels to the far field violates the Second Law of Thermodynamics. Transmission of a large number of channels, each associated with an angular momenta 'twisted wave' mode, to the far field in free space is therefore not po...

These are notes on twisted K-homology theory and twisted Ext-theory from the C *-algebra viewpoint, part of a series of talks on " C *-algebras, noncommutative geometry and K-theory " , primarily for physicists.

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz’s type qBernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz’s type q-zeta functions which interpolate multiple twisted Carlitz’s type q-Euler (Bernoulli) polynomials?” The aim of this paper is to give a part...

It is by now well known that the Poincaré group acts on the Moyal plane with a twisted coproduct. Poincaré invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincaré action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the...

We define the concept of a k-twisted chain in a (directed) graph and the concept of a 2k-twisted graph. We show that for a 2k-twisted graph the set of algebraic 2k-twisted cycles is an integral spanning set for the integral flow module of G. Since a graph is O-twisted if and only if it is strongly connected, our result generalizes the well-known theorem that there is a basis for the flow space ...