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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
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