Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty

The digital transformation of business models in the creative industries: A holistic framework and emerging trends

This paper examines how digital technologies facilitate business model innovations in the creative industries. Through a systematic literature review, a holistic business model framework is developed, which is then used to analyse the empirical evidence from the creative industries. The research found that digital technologies have facilitated pervasive changes in business models, and some significant trends have emerged. However, the reconfigured business models are often not ‘new’ in the unprecedented sense. Business model innovations are primarily reflected in using digital technologies to enable the deployment of a wider range of business models than previously available to a firm. A significant emerging trend is the increasing adoption of multiple business models as a portfolio within one firm. This is happening in firms of all sizes, when one firm uses multiple business models to servedifferent markets segments, sell different products, or engage with multi-sided markets, or to use different business models over time. The holistic business model framework is refined and extended through a recursive learning process, which can serve both as a cognitive instrument for understanding business models and a planning tool for business model innovations. The paper contributes to our understanding of the theory of business models and how digital technologies facilitate business model innovations in the creative industries. Three new themes for future research are highlighted

Matter Effects in Active-Sterile Solar Neutrino Oscillations

The matter effects for solar neutrino oscillations are studied in a general scheme with an arbitrary number of sterile neutrinos, without any constraint on the mixing, assuming only a realistic hierarchy of neutrino squared-mass differences in which the smallest squared-mass difference is effective in solar neutrino oscillations. The validity of the analytic results are illustrated with a numerical solution of the evolution equation in three examples of the possible mixing matrix in the simplest case of four-neutrino mixing.Comment: 26 pages. Final version published in Phys. Rev. D80 (2009) 11300