Fractional quantum Hall states as an Abelian group
  We show that the set of double-layer Fractional Quantum Hall (FQH) states with a given topological order form a finite Abelian group under a new product. This group structure makes it possible to construct new FQH states from known ones. We also introduce a new index which can be used to characterize the topological order of FQH states. 
Ali Nassar
cond-mat.str-el hep-th