2017/08/31 by A. M. Grundland, A. Michel Grundland, A. J. Hariton +1 · 9 citations
Mathematics · Physics and Astronomy · #Affine Lie algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Geometry #Homogeneous space #Infinitesimal #Invariant (physics) #Lie group #Lie superalgebra #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Rational surface #Superalgebra #Supergroup #Surface (topology) #math-ph #math.MP
paper · pdf · doi:10.3390/sym9120318
published in Symmetry 9(12), 318 (Multidisciplinary Digital Publishing Institute) · 29 pages
arxiv created 2017/10/29 · openalex publication_date 2017/12/18 · openalex created_date 2018/01/05 · arxiv updated 2018/01/30 · openalex updated_date 2026/08/05
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.