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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/18780

Title: Braided autoequivalences and quantum commutative bi-Galois objects
Authors: ZHU, Haixing
Zhang, Yinhuo
Issue Date: 2015
Citation: JOURNAL OF PURE AND APPLIED ALGEBRA, 219, p. 4144-4167
Abstract: Let $(H, R)$ be a quasitriangular weak Hopf algebra over a field k. We show that there is a braided monoidal isomorphism between the Yetter–Drinfeld module category $_H^H{YD)$ over H and the category of comodules over some braided Hopf algebra _RH in the category $_HM$. Based on this isomorphism, we prove that every braided bi- Galois object A over the braided Hopf algebra $_RH$ defines a braided autoequivalence of the category $_H^H{YD}$ if and only if A is quantum commutative. In case H is semisimple over an algebraically closed field, i.e. the fusion case, then every braided autoequivalence of $_H^H{YD}$ trivializable on $_HM$ is determined by such a quantum commutative Galois object. The quantum commutative Galois objects in $_HM$ form a group measuring the Brauer group of $(H, R)$ as studied in [21] in the Hopf algebra case.
Notes: Zhu, HX (reprint author), Nanjing Forest Univ, Sch Econ & Management, Longpan Rd 159, Nanjing 210037, Peoples R China. zhuhaixing@163.com; yinhuo.zhang@uhasselt.be
URI: http://hdl.handle.net/1942/18780
DOI: 10.1016/j.jpaa.2015.02.012
ISI #: 000354001200024
ISSN: 0022-4049
Category: A1
Type: Journal Contribution
Validation: ecoom, 2016
Appears in Collections: Research publications

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