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Noether theorem of semisimple Hopf algebra. (Chinese. English summary) Zbl 1126.16004

Summary: Let \(H\) be a finite-dimensional Hopf algebra, \(A\) be an \(H\)-module. This paper gives the definition of Sweedler \(H\)-cohomology, proves that \(H^1(H,A)=0\) when \(H\) is semisimple, which generalizes the classical Noether theorem.

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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