Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 004, 11 pages      arXiv:1510.04408      https://doi.org/10.3842/SIGMA.2016.004

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

Tao Cheng ab, Hua-Lin Huang a and Yuping Yang a
a) School of Mathematics, Shandong University, Jinan 250100, China
b) School of Mathematical Science, Shandong Normal University, Jinan 250014, China

Received October 22, 2015, in final form January 06, 2016; Published online January 12, 2016

Abstract
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.

Key words: generalized Clifford algebra; symmetric Gr-category; twisted group algebra.

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