On the Hopf–Schur group of a field |
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Authors: | Eli Aljadeff Juan Cuadra Shlomo Gelaki Ehud Meir |
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Institution: | 1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel;2. Departamento de Álgebra y Análisis Matemático, Universidad de Almería, E04120 Almería, Spain |
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Abstract: | Let k be any field. We consider the Hopf–Schur group of k, defined as the subgroup of the Brauer group of k consisting of classes that may be represented by homomorphic images of finite-dimensional Hopf algebras over k. We show here that twisted group algebras and abelian extensions of k are quotients of cocommutative and commutative finite-dimensional Hopf algebras over k, respectively. As a consequence we prove that any tensor product of cyclic algebras over k is a quotient of a finite-dimensional Hopf algebra over k, revealing so that the Hopf–Schur group can be much larger than the Schur group of k. |
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