Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition
arXiv:0804.1077 · doi:10.1007/s00220-008-0638-7
Abstract
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.
18 pages, minor corrections after the referee report, retyped in journal format, svjour style, to appear in Communications in Mathematical Physics (2008), dedicated to the memory of L. L. Vaksman (1951-2007), see http://webusers.physics.umn.edu/~duplij/vaksman