Finitely generated invariants of Hopf algebras on free associative algebras
Copyright policy )Finitely generated invariants of Hopf algebras on free associative algebras
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.
- UNIVERSIDADE DE SAO PAULO Brazil
- Universidade de São Paulo Brazil
Numerical Analysis, Algebra and Number Theory, Invariants, Actions of groups and semigroups; invariant theory (associative rings and algebras), free associative algebras, Mathematics - Rings and Algebras, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Hopf algebras (associative rings and algebras), 16S10; 16W30, Rings and Algebras (math.RA), algebras of invariants, FOS: Mathematics, Discrete Mathematics and Combinatorics, group-like elements, Geometry and Topology, Free associative algebras, skew-primitive elements, 16W30, Vector and tensor algebra, theory of invariants, 16S10, Hopf algebra actions
Numerical Analysis, Algebra and Number Theory, Invariants, Actions of groups and semigroups; invariant theory (associative rings and algebras), free associative algebras, Mathematics - Rings and Algebras, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Hopf algebras (associative rings and algebras), 16S10; 16W30, Rings and Algebras (math.RA), algebras of invariants, FOS: Mathematics, Discrete Mathematics and Combinatorics, group-like elements, Geometry and Topology, Free associative algebras, skew-primitive elements, 16W30, Vector and tensor algebra, theory of invariants, 16S10, Hopf algebra actions
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