Classification of two and three dimensional Lie super-bialgebras

Abstract

Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two and three dimensional Lie superalgebras, we obtain and classify all two and three dimensional Lie superbialgebras.

15 pages

References in corpus (3)

• Poisson-Lie T-plurality
• Poisson-Lie T-dual sigma models on supermanifolds
• Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups

Cited by in corpus (17)

• Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions
• String cosmology from Poisson-Lie T-dual sigma models on supermanifolds
• WZW models as mutual super Poisson-Lie T-dual sigma models
• Classification of four and six dimensional Drinfel'd superdoubles
• The gl(1|1) Lie superbialgebras
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Classification of real low dimensional Jacobi(generalized)-Lie bialgebras
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups
• Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ and deformation of related integrable Hamiltonian systems
• Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model