Discrete Minimal Surface Algebras
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining r...
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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146344 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Discrete Minimal Surface Algebras / J. Arnlind, J. Hoppe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146344 |
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irk-123456789-1463442019-02-10T01:24:03Z Discrete Minimal Surface Algebras Arnlind, J. Hoppe, J. We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras. 2010 Article Discrete Minimal Surface Algebras / J. Arnlind, J. Hoppe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R10; 06B15 DOI:10.3842/SIGMA.2010.042 http://dspace.nbuv.gov.ua/handle/123456789/146344 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras. |
| format |
Article |
| author |
Arnlind, J. Hoppe, J. |
| spellingShingle |
Arnlind, J. Hoppe, J. Discrete Minimal Surface Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Arnlind, J. Hoppe, J. |
| author_sort |
Arnlind, J. |
| title |
Discrete Minimal Surface Algebras |
| title_short |
Discrete Minimal Surface Algebras |
| title_full |
Discrete Minimal Surface Algebras |
| title_fullStr |
Discrete Minimal Surface Algebras |
| title_full_unstemmed |
Discrete Minimal Surface Algebras |
| title_sort |
discrete minimal surface algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146344 |
| citation_txt |
Discrete Minimal Surface Algebras / J. Arnlind, J. Hoppe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT arnlindj discreteminimalsurfacealgebras AT hoppej discreteminimalsurfacealgebras |
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2023-05-20T17:24:18Z |
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2023-05-20T17:24:18Z |
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1796153215881838592 |