Geodesic
DERIVED H-MODULE ENDOMORPHISM RINGS
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 649-661

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DOI

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.
DOI : 10.1017/S0017089510000492
Mots-clés : 16E45, 16E40, 16W50 
HE, JI-WEI; OYSTAEYEN, FRED VAN; ZHANG, YINHUO. DERIVED H-MODULE ENDOMORPHISM RINGS. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 649-661. doi: 10.1017/S0017089510000492
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     title = {DERIVED {H-MODULE} {ENDOMORPHISM} {RINGS}},
     journal = {Glasgow mathematical journal},
     pages = {649--661},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000492},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000492/}
}
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