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Finitely generated invariants of Hopf algebras on free associative algebras

Vitor O. Ferreira·Lucia S. I. Murakami
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Abstract

We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the action is scalar. This generalizes an analogous result for group actions by automorphisms obtained by Dicks and Formanek, and Kharchenko.

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Vitor O. Ferreira, Lucia S. I. Murakami. 2005-11-10. Finitely generated invariants of Hopf algebras on free associative algebras. https://arxiv.org/abs/math/0511264

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