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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2016
• Main Authors: Cheng, T., Huang, H.-L., Yang, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2016
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147420
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories / T. Cheng, H.-L. Huang, Y. Yang // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 18 назв. — англ.

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.