Chen, Quanguo; Tang, Jiangang Trace function in weak Hopf algebra. (Chinese. English summary) Zbl 1224.16062 J. Yantai Univ., Nat. Sci. Eng. 23, No. 3, 169-171 (2010). Summary: Based on the discussion of D. Nikshych [Adv. Math. 170, No. 2, 257-286 (2002; Zbl 1010.16041)] of the relationships of the dual pair of the left integral, further studies are made and two conclusions: \(S^{-1}(l)=l\leftarrow\alpha\), \(\lambda\leftarrow g=\lambda\circ S^{-1}\) are obtained in this paper. Besides, based on the two conclusions above and the integral theory in weak Hopf algebras, the traces of morphisms in \(\text{End}_k(H)\) are discussed in weak Hopf algebra setting and some meaningful findings are presented in the form of theorem and corollary so as to generalize what D. E. Radford [J. Algebra 163, No. 3, 583-622 (1994; Zbl 0801.16039)] has achieved in the ordinary Hopf algebra setting. MSC: 16T05 Hopf algebras and their applications Keywords:weak Hopf algebras; trace functions; left integrals Citations:Zbl 1010.16041; Zbl 0801.16039 PDFBibTeX XMLCite \textit{Q. Chen} and \textit{J. Tang}, J. Yantai Univ., Nat. Sci. Eng. 23, No. 3, 169--171 (2010; Zbl 1224.16062)