Algebraic Aspects of the Supersymmetric Minimal Surface Equation
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugac...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/9/12/318 |
| _version_ | 1798041879436066816 |
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| author | Alfred Michel Grundland Alexander Hariton |
| author_facet | Alfred Michel Grundland Alexander Hariton |
| author_sort | Alfred Michel Grundland |
| collection | DOAJ |
| description | In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version. |
| first_indexed | 2024-04-11T22:27:42Z |
| format | Article |
| id | doaj.art-aa6cfc7fbf3c4c3ba92abe443ebab68a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:27:42Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-aa6cfc7fbf3c4c3ba92abe443ebab68a2022-12-22T03:59:36ZengMDPI AGSymmetry2073-89942017-12-0191231810.3390/sym9120318sym9120318Algebraic Aspects of the Supersymmetric Minimal Surface EquationAlfred Michel Grundland0Alexander Hariton1Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, QC H3C 3J7, CanadaCentre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, QC H3C 3J7, CanadaIn this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version.https://www.mdpi.com/2073-8994/9/12/318supersymmetric modelsLie subalgebrassymmetry reductionconformally parameterized surfaces |
| spellingShingle | Alfred Michel Grundland Alexander Hariton Algebraic Aspects of the Supersymmetric Minimal Surface Equation Symmetry supersymmetric models Lie subalgebras symmetry reduction conformally parameterized surfaces |
| title | Algebraic Aspects of the Supersymmetric Minimal Surface Equation |
| title_full | Algebraic Aspects of the Supersymmetric Minimal Surface Equation |
| title_fullStr | Algebraic Aspects of the Supersymmetric Minimal Surface Equation |
| title_full_unstemmed | Algebraic Aspects of the Supersymmetric Minimal Surface Equation |
| title_short | Algebraic Aspects of the Supersymmetric Minimal Surface Equation |
| title_sort | algebraic aspects of the supersymmetric minimal surface equation |
| topic | supersymmetric models Lie subalgebras symmetry reduction conformally parameterized surfaces |
| url | https://www.mdpi.com/2073-8994/9/12/318 |
| work_keys_str_mv | AT alfredmichelgrundland algebraicaspectsofthesupersymmetricminimalsurfaceequation AT alexanderhariton algebraicaspectsofthesupersymmetricminimalsurfaceequation |