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DERIVED H-MODULE ENDOMORPHISM RINGS

Published online by Cambridge University Press:  25 August 2010

JI-WEI HE ,
FRED VAN OYSTAEYEN  and
YINHUO ZHANG
JI-WEI HE
Affiliation:
Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium e-mail: jwhe@usx.edu.cn
FRED VAN OYSTAEYEN
Affiliation:
Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium e-mail: fred.vanoystaeyen@ua.ac.be
YINHUO ZHANG
Affiliation:
Department WNI, University of Hasselt, 3590 Diepenbeek, Belgium e-mail: yinhuo.zhang@uhasselt.be
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Abstract

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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⋅ ∈ D(A) may be regarded as an object in D(B) via the restriction functor. We discuss the relations of the derived endomorphism rings EA(M⋅) = ⊕i∈ℤHomD(A)(M⋅, M⋅[i]) and EB(M⋅) = ⊕i∈ℤHomD(B)(M⋅, M⋅[i]). If H is a finite-dimensional semi-simple Hopf algebra, then EA(M⋅) is a graded sub-algebra of EB(M⋅). In particular, if M is a usual A-module, a necessary and sufficient condition for EB(M) to be an H*-Galois graded extension of EA(M) is obtained. As an application of the results, we show that the Koszul property is preserved under Hopf Galois graded extensions.

Keywords

16E4516E4016W50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 649 - 661
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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