The gl(1|1) Lie Superbialgebras

Details The gl(1|1) Lie Superbialgebras The gl(1|1) Lie Superbialgebras

2011-12-03

arxiv.org/abs/1112.0652v1

Physics

Mathematical Physics

17 pages, 7 tables

Scientific paper

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. Finally, we classify Drinfel'd superdoubles generated by the gl(1|1) Lie superbialgebras.

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