اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDerived $H$-module endomorphism rings
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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 $M^cdotin D(A)$ may be regarded as an object in $D(B)$ via the restriction functor. We discuss the relations of the derived endomorphism rings $E_A(M^cdot)=op_{iinmathbb{Z}}Hom_{D(A)}(M^cdot,M^cdot[i])$ and $E_B(M^cdot)=op_{iinmathbb{Z}}Hom_{D(B)}(M^cdot,M^cdot[i])$. If $H$ is a finite dimensional semisimple Hopf algebra, then $E_A(M^cdot)$ is a graded subalgebra of $E_B(M^cdot)$. 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.
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It is proved that if A_p is a countable elementary abelian p-group, then: (i) The ring End(A_p) does not admit a nondiscrete locally compact ring topology. (ii) Under (CH) the simple ring End(A_p)/I, where I is the ideal of End(A_p) consisting of all
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