Geodesic
Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants
Andrzej Tyc1
1 Faculty of Mathematics and Informatics N. Copernicus University Chopina 12/18 87-100 Toruń, Poland
Colloquium Mathematicum, Tome 88 (2001) no. 1, pp. 39-55 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $H$ be a Hopf algebra over a field $k$ such that every finite-dimensional (left) $H$-module is semisimple. We give a counterpart of the first fundamental theorem of the classical invariant theory for locally finite, finitely generated (commutative) $H$-module algebras, and for local, complete $H$-module algebras. Also, we prove that if $H$ acts on the $k$-algebra $A=k[[X_{1},\dots,X_{n}]]$ in such a way that the unique maximal ideal in $A$ is invariant, then the algebra of invariants $A^{H}$ is a noetherian Cohen–Macaulay ring.
DOI : 10.4064/cm88-1-5
Keywords: hopf algebra field every finite dimensional h module semisimple counterpart first fundamental theorem classical invariant theory locally finite finitely generated commutative h module algebras local complete h module algebras prove acts k algebra dots unique maximal ideal invariant algebra invariants noetherian cohen macaulay ring

Andrzej Tyc 1

1 Faculty of Mathematics and Informatics N. Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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Andrzej Tyc. Actions of Hopf algebras on pro-semisimple
noetherian algebras and their invariants. Colloquium Mathematicum, Tome 88 (2001) no. 1, pp. 39-55. doi: 10.4064/cm88-1-5

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