A conjecture for the algorithmic decomposition of paths over an SU(3) ADE graph
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| Format: | Artículo científico |
| Sprache: | en |
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Sociedad Mexicana de Física A.C.
2015
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| _version_ | 1876441796047798272 |
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| author | J.A. Pineda |
| author_facet | J.A. Pineda |
| contents | A conjecture for the algorithmic decomposition of paths over an SU(3) ADE graph J.A. Pineda E. Isasi M.I. Caicedo Física, Astronomía y Matemáticas Lieb algebra graph theory Ocenanu cells quantum groups essential paths Through a geometric understanding of the creation, cap, annihilation and cup operators for ADE graphs in SU(3) we propose the first steps towards an algorithm that would allow one to write an arbitrary elementary path as an ordered combination of creation and cap operators acting upon an essential path. We propose a sketch of a proof and use our proposal for some examples for the A2 and E5 graphs of the SU(3) family. Attaining this decomposition is an important step in obtaining the path formulation of the quantum Algebra of a modular invariant RCFT. 2015 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57042691007 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.6 Vol.61 |
| format | Artículo científico |
| id | redalyc_57042691007 |
| institution | Redalyc |
| language | en |
| publishDate | 2015 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | A conjecture for the algorithmic decomposition of paths over an SU(3) ADE graph J.A. Pineda Física, Astronomía y Matemáticas Lieb algebra graph theory Ocenanu cells quantum groups essential paths A conjecture for the algorithmic decomposition of paths over an SU(3) ADE graph J.A. Pineda E. Isasi M.I. Caicedo Física, Astronomía y Matemáticas Lieb algebra graph theory Ocenanu cells quantum groups essential paths Through a geometric understanding of the creation, cap, annihilation and cup operators for ADE graphs in SU(3) we propose the first steps towards an algorithm that would allow one to write an arbitrary elementary path as an ordered combination of creation and cap operators acting upon an essential path. We propose a sketch of a proof and use our proposal for some examples for the A2 and E5 graphs of the SU(3) family. Attaining this decomposition is an important step in obtaining the path formulation of the quantum Algebra of a modular invariant RCFT. 2015 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57042691007 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.6 Vol.61 |
| title | A conjecture for the algorithmic decomposition of paths over an SU(3) ADE graph |
| topic | Física, Astronomía y Matemáticas Lieb algebra graph theory Ocenanu cells quantum groups essential paths |
| url | https://www.redalyc.org/articulo.oa?id=57042691007 |