Geodesic
Invariants of the action of a~semisimple Hopf algebra on PI-algebra
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 21-34.

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We extend classical results in the invariant theory of finite groups to the action of a finite-dimensional Hopf algebra $H$ on an algebra satisfying a polynomial identity. In particular, we prove that an $H$-module algebra $A$ over an algebraically closed field $\mathbf k$ is integral over the subalgebra of invariants, if $H$ is a semisimple and cosemisimple Hopf algebra. We show that if $\operatorname{char}\mathbf k>0$, then the algebra $Z(A)^{H_0}$ is integral over the subalgebra of central invariants $Z(A)^H$, where $Z(A)$ is the center of algebra $A$, $H_0$ is the coradical of $H$. This result allowed to prove that the algebra $A$ is integral over the subalgebra $Z(A)^H$ in some special case. We also construct a counterexample to the integrality of the algebra $A^{H_0}$ over the subalgebra of invariants $A^H$ for a pointed Hopf algebra over a field of non-zero characteristic.
Keywords: Hopf algebras, invariant theory, PI-algebras, rings of quotients, coradical. 
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M. S. Eryashkin. Invariants of the action of a~semisimple Hopf algebra on PI-algebra. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2016), pp. 21-34. http://geodesic.mathdoc.fr/item/IVM_2016_8_a2/

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