Abstract
In this paper we extend classical results of the invariant theory of finite groups to the action of a finite-dimensional semisimple Hopf algebra H on a special algebra A, which is homomorphically mapped onto a commutative integral domain, and the kernel of this map contains no nonzero H-stable ideals. We prove that the algebra A is finitely generated as a module over a subalgebra of invariants, and the latter is finitely generated as a k-algebra. We give a counterexample to the finite generation of a non-semisimple Hopf algebra.
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Original Russian Text © M.S. Eryashkin, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 8, pp. 14–22.
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Eryashkin, M.S. Invariants of the action of a semisimple finite-dimensional Hopf algebra on special algebras. Russ Math. 55, 11–18 (2011). https://doi.org/10.3103/S1066369X11080032
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DOI: https://doi.org/10.3103/S1066369X11080032