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arXiv · 0804.1077

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

Steven Duplij·Sergey Sinel'shchikov
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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.

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Steven Duplij, Sergey Sinel'shchikov. 2008-06-19. Quantum enveloping algebras with von Neumann regular Cartan-like generators and the Pierce decomposition. https://doi.org/10.1007/s00220-008-0638-7

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