Finitely generated invariants of Hopf algebras on free associative algebras

2005/11/10 by Vitor O. Ferreira, Lucia S. I. Murakami, Ferreira, Vitor O. +1
Mathematics · #16S10 #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:16S10 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0511264

arxiv created 2005/11/10 · openalex publication_date 2005/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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• Invariants of finite Hopf algebras
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• Invariants of finite groups acting on (free) skew fields
• Subrings of invariants for actions of finite dimensional Hopf algebras