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[[X₁,...,Xₙ]] in such a way that the unique maximal ideal in A is invariant, then the algebra of invariants is a noetherian Cohen-Macaulay ring.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-1-5,
author = {Andrzej Tyc},
title = {Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {39-55},
zbl = {0973.16024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-1-5}
}
Andrzej Tyc. Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants. Colloquium Mathematicae, Tome 89 (2001) pp. 39-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-1-5/