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

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 $p^3$ and $p^4$ for any prime number $p.$Comment: 12 pages; Minor revision according to the referee's suggestio

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

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

The Green rings of pointed tensor categories of finite type

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