1112.0652 (A. Eghbali et al.)

The gl(1|1) Lie superbialgebras    [PDF]

A. Eghbali, A. Rezaei-Aghdam

By direct calculations of matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation, and using the automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and classify all gl(1|1) Lie superbialgebras. Then, by calculating their classical r-matrices, the gl(1|1) coboundary Lie superbialgebras and their types (triangular, quasi-triangular or factorizable) are determined, furthermore in this way super Poisson structures on the GL(1|1) Lie supergroup are obtained. Also, we classify Drinfeld superdoubles based on the gl(1|1) as a theorem. Finally, as a physical application of the coboundary Lie superbialgebras, we construct a new integrable system on the homogeneous superspace OSp(1|2)/U(1).

View original: http://arxiv.org/abs/1112.0652