Abstract
Let H be a weak Hopf algebra (quantum groupoid) in the sense of [1]. Then in this note we first introduce weak Drinfeld double D(H) and character algebra C(H) of H. Next we define a weak D(H)-module algebra and a C(H)-module on C H (H S ), the centralizer of H S . Finally we prove that if H is a semisimple weak Hopf algebra over an algebraically closed field k of characteristic 0, then the action of D(H) on C H (H S ) and the action of C(H) on C H (H S ) form a commuting pair, which generalizes the main result in [11].
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Shen, Bl. (2013). A Commuting Pair in Quantum Qroupoids. In: Yang, Y., Ma, M., Liu, B. (eds) Information Computing and Applications. ICICA 2013. Communications in Computer and Information Science, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53703-5_63
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DOI: https://doi.org/10.1007/978-3-642-53703-5_63
Publisher Name: Springer, Berlin, Heidelberg
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