Liu, Junli; Yang, Shilin Weak Hopf superalgebras \(\text{wsl}_q^{\text{d}}(m|n)\). (Chinese. English summary) Zbl 1199.16071 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 70-86 (2009). 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 Keywords:weak antipodes; PBW bases; weak Hopf superalgebras PDFBibTeX XMLCite \textit{J. Liu} and \textit{S. Yang}, Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 70--86 (2009; Zbl 1199.16071)