Algebraic Aspects of the Supersymmetric Minimal Surface Equation
by
Alfred Michel Grundland 1,2,* and Alexander Hariton 1
Alfred Michel Grundland 1,2,* and Alexander Hariton 1
1
Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, QC H3C 3J7, Canada
2
Département de mathématiques et d’informatique, Université du Québec, C.P. 500, Trois-Rivières, QC G9A 5H7, Canada
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(12), 318; https://doi.org/10.3390/sym9120318
Received: 13 November 2017 / Revised: 8 December 2017 / Accepted: 13 December 2017 / Published: 18 December 2017
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.
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Keywords:
supersymmetric models; Lie subalgebras; symmetry reduction; conformally parameterized surfaces
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MDPI and ACS Style
Grundland, A.M.; Hariton, A. Algebraic Aspects of the Supersymmetric Minimal Surface Equation. Symmetry 2017, 9, 318.
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