1,175 research outputs found
Quasi-Quantum Planes and Quasi-Quantum Groups of Dimension and
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 and for any prime
number 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
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