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Weak Hopf superalgebras \(\text{wsl}_q^{\text{d}}(m|n)\). (Chinese. English summary) Zbl 1199.16071

Summary: Along the idea of definition of a weak Hopf algebra in the sense of a bialgebra attached with a weak antipode, we give a definition of weak Hopf superalgebra. As an example, a class of weak Hopf superalgebras but not Hopf superalgebras \(\text{wsl}_q^{\text{d}}(m|n)\) is constructed. A PBW basis of \(\text{wsl}_q^{\text{d}}(m|n)\) is described.

MSC:

16T10 Bialgebras
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W55 “Super” (or “skew”) structure
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