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Trace function in weak Hopf algebra. (Chinese. English summary) Zbl 1224.16062

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
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