Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants

Andrzej Tyc. "Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants." Colloquium Mathematicae 88.1 (2001): 39-55. <http://eudml.org/doc/283456>.

@article{AndrzejTyc2001,
abstract = {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 $A^\{H\}$ is a noetherian Cohen-Macaulay ring.},
author = {Andrzej Tyc},
journal = {Colloquium Mathematicae},
keywords = {invariant theory; finitely semisimple Hopf algebras; Reynolds operators; Hopf algebra actions; pro-semisimple Hopf module algebras; Artin-Rees property; Cohen-Macaulay rings; algebras of invariants; locally finite Hopf module algebras; Noetherian algebras},
language = {eng},
number = {1},
pages = {39-55},
title = {Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants},
url = {http://eudml.org/doc/283456},
volume = {88},
year = {2001},
}

TY - JOUR
AU - Andrzej Tyc
TI - Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants
JO - Colloquium Mathematicae
PY - 2001
VL - 88
IS - 1
SP - 39
EP - 55
AB - 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 $A^{H}$ is a noetherian Cohen-Macaulay ring.
LA - eng
KW - invariant theory; finitely semisimple Hopf algebras; Reynolds operators; Hopf algebra actions; pro-semisimple Hopf module algebras; Artin-Rees property; Cohen-Macaulay rings; algebras of invariants; locally finite Hopf module algebras; Noetherian algebras
UR - http://eudml.org/doc/283456
ER -