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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.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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Cheng, T. Huang, H.-L. Yang, Y. 2019-02-14T18:16:56Z 2019-02-14T18:16:56Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147420 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. This research was supported by SRFDP 20130131110001, NSFC 11471186, NSFC 11571199, and SDNSF ZR2013AM022. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
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| title |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories |
| spellingShingle |
Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories Cheng, T. Huang, H.-L. Yang, Y. |
| 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 |
| author |
Cheng, T. Huang, H.-L. Yang, Y. |
| author_facet |
Cheng, T. Huang, H.-L. Yang, Y. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT chengt generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories AT huanghl generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories AT yangy generalizedcliffordalgebrasasalgebrasinsuitablesymmetriclineargrcategories |
| first_indexed |
2025-12-07T16:12:01Z |
| last_indexed |
2025-12-07T16:12:01Z |
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1850866580746928128 |