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Weak Hopf algebras corresponding to \(U_q[\text{sl}_n]\). (English) Zbl 1063.16041

Summary: We investigate the weak Hopf algebras of Li based on \(U_q[\text{sl}_n]\) and Sweedler’s finite dimensional example. We give weak Hopf algebra isomorphisms between the weak generalizations of \(U_q[\text{sl}_n]\) which are “upgraded” automorphisms of \(U_q[\text{sl}_n]\) and hence give a classification of these structures as weak Hopf algebras. We also show how to decompose these examples into a direct sum which leads to unexpected isomorphisms between their algebraic structure.

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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