Quantum enveloping algebras with von Neumann regular Cartan-like   generators and the Pierce decomposition
  Quantum bialgebras derivable from Uq(sl2) which contain idempotents and von Neumann regular Cartan-like generators are introduced and investigated. Various types of antipodes (invertible and von Neumann regular) on these bialgebras are constructed, which leads to a Hopf algebra structure and a von Neumann-Hopf algebra structure, respectively. For them, explicit forms of some particular R-matrices (also, invertible and von Neumann regular) are presented, and the latter respects the Pierce decomposition. 
Steven Duplij (Institute of Theoretical Physics, Cologne University)   and Sergey Sinel'shchikov (Institute for Low Temperat...