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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11290

Authors: He, Ji-Wei
Van Oystaeyen, Fred
ZHANG, Yinhuo
Issue Date: 2010
Citation: GLASGOW MATHEMATICAL JOURNAL, 52. p. 649-661
Abstract: Let H be a Hopf algebra, A/B be an H-Galois extension. Let D(A) and D(B) be the derived categories of right A-modules and of right B-modules, respectively. An object M-. is an element of D(A) may be regarded as an object in D(B) via the restriction functor. We discuss the relations of the derived endomorphism rings E-A(M-.) =. circle plus i is an element of zHom(D(A))(M-. , M-. [i]) and E-B(M-.) = circle plus i is an element of z Hom(D(B))(M-., M-. [i]). If H is a finite-dimensional semi-simple Hopf algebra, then E-A(M-.) is a graded sub-algebra of E-B(M-.). In particular, if M is a usual A-module, a necessary and sufficient condition for E-B(M) to be an H*-Galois graded extension of E-A(M) is obtained. As an application of the results, we show that the Koszul property is preserved under Hopf Galois graded extensions.
Notes: [He, Ji-Wei] Shaoxing Coll Arts & Sci, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China. [He, Ji-Wei; Van Oystaeyen, Fred] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium. [Zhang, Yinhuo] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium. jwhe@usx.edu.cn; fred.vanoystaeyen@ua.ac.be; yinhuo.zhang@uhasselt.be
URI: http://hdl.handle.net/1942/11290
DOI: 10.1017/S0017089510000492
ISI #: 000282230200020
ISSN: 0017-0895
Category: A1
Type: Journal Contribution
Validation: ecoom, 2011
Appears in Collections: Research publications

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