Duals and doubles of quantum groupoids (\(\times_R\)-Hopf algebras) (Q2708921)

\(\times_R\)-bialgebras were introduced as a generalization of the notion of bialgebra by \textit{M. Takeuchi} [J. Math. Soc. Japan 29, 459-492 (1977; Zbl 0349.16012)] and with a different motivation by \textit{J.-H. Lu} [Int. J. Math. 7, No. 1, 47-70 (1996; Zbl 0884.17010)]. A notion of \(\times_R\)-Hopf algebra is introduced in the paper under review. Also the notions of Yetter-Drinfeld module, skew pairing, dual, Drinfeld double are generalized to the theory of \(\times_R\)-bialgebras. Several results known for usual bialgebras and Hopf algebras are generalized to this setting.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00038].