Geodesic
Invariants of the action of a~semisimple finite-dimensional Hopf algebra on special algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 14-22

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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 ideal. 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 $\mathbf k$-algebra. We give a counterexample for the finite generation of a non-semisimple Hopf algebra.
Keywords: Hopf algebras, invariant rings. 
@article{IVM_2011_8_a2,
     author = {M. S. Eryashkin},
     title = {Invariants of the action of a~semisimple finite-dimensional {Hopf} algebra on special algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {14--22},
     publisher = {mathdoc},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_8_a2/}
}
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M. S. Eryashkin. Invariants of the action of a~semisimple finite-dimensional Hopf algebra on special algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2011), pp. 14-22. http://geodesic.mathdoc.fr/item/IVM_2011_8_a2/