Matrix Bases for Star Products: a Review
We review the matrix bases for a family of noncommutative ⋆ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146614 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Matrix Bases for Star Products: a Review / F. Lizzi, P. Vitale // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 83 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862721133781975040 |
|---|---|
| author | Lizzi, F. Vitale, P. |
| author_facet | Lizzi, F. Vitale, P. |
| citation_txt | Matrix Bases for Star Products: a Review / F. Lizzi, P. Vitale // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 83 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review the matrix bases for a family of noncommutative ⋆ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity.
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| first_indexed | 2025-12-07T18:28:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146614 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:28:56Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lizzi, F. Vitale, P. 2019-02-10T10:04:21Z 2019-02-10T10:04:21Z 2014 Matrix Bases for Star Products: a Review / F. Lizzi, P. Vitale // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 83 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58Bxx; 40C05; 46L65 DOI:10.3842/SIGMA.2014.086 https://nasplib.isofts.kiev.ua/handle/123456789/146614 We review the matrix bases for a family of noncommutative ⋆ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html. 
 We were partially supported by UniNA and Compagnia di San Paolo under the grant “Programma
 STAR 2013”. F. Lizzi acknowledges support by CUR Generalitat de Catalunya under
 project FPA2010-20807. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Matrix Bases for Star Products: a Review Article published earlier |
| spellingShingle | Matrix Bases for Star Products: a Review Lizzi, F. Vitale, P. |
| title | Matrix Bases for Star Products: a Review |
| title_full | Matrix Bases for Star Products: a Review |
| title_fullStr | Matrix Bases for Star Products: a Review |
| title_full_unstemmed | Matrix Bases for Star Products: a Review |
| title_short | Matrix Bases for Star Products: a Review |
| title_sort | matrix bases for star products: a review |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146614 |
| work_keys_str_mv | AT lizzif matrixbasesforstarproductsareview AT vitalep matrixbasesforstarproductsareview |