Classification of Low Dimensional Lie Super-Bialgebras

Abstract

A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification of equivalent structures is applied. In all the cases Poisson-Lie brackets on supergroups are found. Possibility of quantizing them in order to obtain quantum groups is discussed. It turns out to be straightforward for all but one structures for super-E(2) group.

15 pages, LaTeX

References in corpus (4)

• Lie bialgebra quantizations of the oscillator algebra and their universal $R$--matrices
• Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson Counterparts
• Twist Deformation of the rank one Lie Superalgebra
• Quantum E(2) groups and Lie bialgebra structures

Cited by in corpus (13)

• Poisson-Lie T-dual sigma models on supermanifolds
• Classification of two and three dimensional Lie super-bialgebras
• Noncommutative Geometry of Super-Jordanian $OS{p}_h(2/1)$ Covariant Quantum Space
• Classification of four and six dimensional Drinfel'd superdoubles
• The gl(1|1) Lie superbialgebras
• Super-Jordanian Quantum Superalgebra ${\mathcal{U}}_h(osp(2/1))$
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• Lie superbialgebra structures on the Lie superalgebra $({\mathcal{C}}^3+\mathcal{A})$ and deformation of related integrable Hamiltonian systems
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter deformations of the OSP(1|2) WZW model