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

Colloquium Mathematicae (2001)

- Volume: 88, Issue: 1, page 39-55
- ISSN: 0010-1354

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topAndrzej 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 -

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