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Quantum integrals and the affineness criterion for quantum Yetter-Drinfeld π-modules
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In the paper, the quantum integrals associated to quantum Yetter-Drinfeld
?-modules are defined. We shall prove the following affineness criterion: if
there exists ? = {?? : H? ? Hom(H?-1, A)} ? ? ? a total quantum integral and
the canonical map ? : A?B A ? ???? H? ? A, ?(a?B b)= ???? S?-1
??(b[1,?-1?-1?])b[0,0]<-1,?> ? ab[0,0]<0,0> is subjective. Then the
induction functor -?B A : UB ? H YD?A is an equivalence of categories. The
affineness criterion proven by Menini and Militaru is recovered as special
cases.
Title: Quantum integrals and the affineness criterion for quantum Yetter-Drinfeld π-modules
Description:
In the paper, the quantum integrals associated to quantum Yetter-Drinfeld
?-modules are defined.
We shall prove the following affineness criterion: if
there exists ? = {?? : H? ? Hom(H?-1, A)} ? ? ? a total quantum integral and
the canonical map ? : A?B A ? ???? H? ? A, ?(a?B b)= ???? S?-1
??(b[1,?-1?-1?])b[0,0]<-1,?> ? ab[0,0]<0,0> is subjective.
Then the
induction functor -?B A : UB ? H YD?A is an equivalence of categories.
The
affineness criterion proven by Menini and Militaru is recovered as special
cases.
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