783 research outputs found

    Quasi-Quantum Planes and Quasi-Quantum Groups of Dimension p3p^3 and p4p^4

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    The aim of this paper is to contribute more examples and classification results of finite pointed quasi-quantum groups within the quiver framework initiated in \cite{qha1, qha2}. The focus is put on finite dimensional graded Majid algebras generated by group-like elements and two skew-primitive elements which are mutually skew-commutative. Such quasi-quantum groups are associated to quasi-quantum planes in the sense of nonassociative geomertry \cite{m1, m2}. As an application, we obtain an explicit classification of graded pointed Majid algebras with abelian coradical of dimension p3p^3 and p4p^4 for any prime number p.p.Comment: 12 pages; Minor revision according to the referee's suggestio

    Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories

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    By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper is to study generalized Clifford algebras in a similar manner and extend the results of Albuquerque, Majid and Bulacu to the generalized setting. In particular, by taking full advantage of the gauge transformations in symmetric linear Gr-categories, we derive the decomposition theorem and provide categorical weak Hopf structures for generalized Clifford algebras in a conceptual and simpler manner

    Stress study in faulted tunnel models by combined photoelastic measurements and finite element analysis

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    An investigation is performed to develop a proper technique for analyzing the stresses in and around three adjacent scaled tunnel models, along with the stress concentration factors resulting from the existence of a fault that penetrates two of the three tunnels, at an inclined angle; Photoelasticity and Finite Element method, are used in this investigation. The Photoelastic measurements are performed by using a plexiglass plane model. Concurrent simulations of the same plexiglass model are performed by the Finite Element analysis. The principal stress patterns are measured by both methods, and the stress concentration factors are calculated at predetermined points. Results from both the Photoelastic models and the Finite Element models are compared to each other at each step of the investigation; A conclusion can be made that, the Finite Element techniques used in this research are reliable and fully capable of representing a faulted tunnel system

    The Green rings of pointed tensor categories of finite type

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    In this paper, we compute the Clebsch-Gordan formulae and the Green rings of connected pointed tensor categories of finite type.Comment: 14 page
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