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...
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| Datum: | 2016 |
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| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147420 |
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| Zitieren: | 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. |
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irk-123456789-1474202019-02-24T14:10:54Z Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories Cheng, T. Huang, H.-L. Yang, Y. 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. 2016 Article 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. 1815-0659 2010 Mathematics Subject Classification: 15A66; 18D10; 16S35 DOI:10.3842/SIGMA.2016.004 http://dspace.nbuv.gov.ua/handle/123456789/147420 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
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. |
| format |
Article |
| author |
Cheng, T. Huang, H.-L. Yang, Y. |
| spellingShingle |
Cheng, T. Huang, H.-L. Yang, Y. Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cheng, T. Huang, H.-L. Yang, Y. |
| author_sort |
Cheng, T. |
| title |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| title_short |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| title_full |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| title_fullStr |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| title_full_unstemmed |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| title_sort |
generalized clifford algebras as algebras in suitable symmetric linear gr-categories |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147420 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT chengt generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories AT huanghl generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories AT yangy generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories |
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2025-07-11T02:02:30Z |
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2025-07-11T02:02:30Z |
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