A classification of four-dimensional Lie superalgebras

DOI10.1063/1.523598zbMath0421.17002OpenAlexW2014234974MaRDI QIDQ3853803

N. B. Backhouse

Publication date: 1978

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.523598

zbMATH Keywords

commutation relationsLie superalgebras

Mathematics Subject Classification ID

Superalgebras (17A70)

Related Items (21)

Cosmological string backgrounds from super Poisson-Lie T-plurality ⋮ Lie superbialgebra structures on the Lie superalgebra C3+A and deformation of related integrable Hamiltonian systems ⋮ Classification of the five-dimensional Lie superalgebras over the real numbers ⋮ Classical \(r\)-matrices of two- and three-dimensional Lie superbialgebras and their Poisson-Lie supergroups ⋮ Quadratic symplectic Lie superalgebras with a filiform module as an odd part ⋮ Symplectic double extensions for restricted quasi-Frobenius Lie (super)algebras ⋮ Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras ⋮ Yang-Baxter deformation of WZW model based on Lie supergroups: the cases of \(GL(1|1)\) and \((C^3 + A)\) ⋮ Unnamed Item ⋮ Characterization of contact Lie superalgebras ⋮ Super Poisson-Lie symmetry of the \(GL(1|1)\) WZNW model and worldsheet boundary conditions ⋮ Solution of the equations of motion for a super non-abelian sigma model in curved background by the super Poisson-Lie T-duality ⋮ String cosmology from Poisson-Lie T-dual sigma models on supermanifolds ⋮ On degenerations of Lie superalgebras ⋮ Moduli spaces of low-dimensional Lie superalgebras ⋮ WZW models as mutual super Poisson-Lie T-dual sigma models ⋮ Fock space representations of the Lie superalgebra A(0,n) ⋮ Boson, para-boson, and boson-fermion representations of some graded Lie algebras ⋮ Drinfel’d superdoubles and Poisson–Lie T-plurality in low dimensions ⋮ Classification of two and three dimensional Lie superbialgebras ⋮ Classification of four and six dimensional Drinfel’d superdoubles

Cites Work

• Classification of some 2-graded Lie algebras
• Representation theory for symplectic 2-graded Lie algebras
• Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
• Semisimple graded Lie algebras
• On the structure of simple pseudo Lie algebras and their invariant bilinear forms
• Classification of all simple graded Lie algebras whose Lie algebra is reductive. I
• Classification of all simple graded Lie algebras whose Lie algebra is reductive. II. Construction of the exceptional algebras
• Graded Lie algebras: Generalization of Hermitian representations
• Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras
• Invariants of real low dimension Lie algebras
• Simple supersymmetries
• Lie superalgebras

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