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arXiv · 1907.10527

Affine commutative-by-finite Hopf algebras

Kenneth Brown·Miguel Couto
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Abstract

The objects of study in this paper are Hopf algebras $H$ which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra by a finite dimensional Hopf algebra. Basic structural and homological properties are recalled and classes of examples are listed. Bounds are obtained on the dimensions of simple $H$-modules, and the structure of $H$ is shown to be severely constrained when the finite dimensional extension is semisimple and cosemisimple.

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Kenneth Brown, Miguel Couto. 2019-07-24. Affine commutative-by-finite Hopf algebras. https://arxiv.org/abs/1907.10527

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