Abstract
LetH be a commutative, cocommutative and faithfully projective Hopf algebra over a commutative ringR. Using cohomological methods, we obtain a description of a subgroup of Long’s Brauer group ofH-dimodule algebras:Ψ where the mapψ is induced by the smash product, and where BDs (R, H) is the subgroup of the Brauer-Long group consisting of all elements which are split by a faithfully flat extension ofR. As an example, the Brauer-Long group of a free Hopf algebra of rank 2 is computed. The results are also applied to Orzech’s subgroup of the Brauer-Long group.
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