Abstract
Quantum bialgebras derivable from U q (sl 2) 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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Communicated by A. Connes
Dedicated to the memory of our colleague Leonid L. Vaksman (1951–2007)
On leave of absence from: TheoryGroup, Nuclear Physics Laboratory,V.N.Karazin Kharkov National University, Svoboda Sq. 4, Kharkov 61077, Ukraine. E-mail: sduplij@gmail.com; http://webusers.physics.umn.edu/~duplij
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Duplij, S., Sinel’shchikov, S. Quantum Enveloping Algebras with von Neumann Regular Cartan-like Generators and the Pierce Decomposition. Commun. Math. Phys. 287, 769–785 (2009). https://doi.org/10.1007/s00220-008-0638-7
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DOI: https://doi.org/10.1007/s00220-008-0638-7