  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.
