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We present a rich source of Hopf algebras starting from a cofinite centralextension of a Noetherian Hopf algebra and a subgroup of the algebraic group ofcharacters of the central Hopf subalgebra. The construction is transparent froma Tannakian perspective. We determine when the new Hopf algebras areco-Frobenius, or cosemisimple, or Noetherian, or regular, or have finiteGelfand-Kirillov dimension.

A class of finite-by-cocommutative Hopf algebras