Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition

Details Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition

2008-04-07

arxiv.org/abs/0804.1077v3

Communications in Mathematical Physics, - 2009. - V. 287. - No. 4. - P. 769-785

Mathematics

Quantum Algebra

18 pages, minor corrections after the referee report, retyped in journal format, svjour style, to appear in Communications in

Scientific paper

10.1007/s00220-008-0638-7

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.

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