Classification of the quantum deformation of the superalgebra $GL(1|1)$

Details Classification of the quantum deformation of the superalgebra $GL(1|1)$ Classification of the quantum deformation of the superalgebra $GL(1|1)$

1997-05-27

arxiv.org/abs/q-alg/9705024v2

Mathematics

Quantum Algebra

23p LaTeX2e Document - packages amsfonts,subeqn - misprints and errors corrected, one section added

Scientific paper

10.1088/0305-4470/31/17/014

We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each $R$ matrix, one finds two inequivalent coproducts whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra $gl(1|1)$ for suitable limits of the deformation parameters but this is no longer true in the unbraided case.

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