Persistent Link:
http://hdl.handle.net/10150/186000
Title:
Computation of polynomial invariants of finite groups.
Author:
McShane, Janet Marie.
Issue Date:
1992
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
If G is a finite subgroup of GL(n,K), K a field of characteristic 0, it is well known that the algebra I of polynomial invariants of G is Cohen-Macaulay. Consequently I has a subalgebra J of Krull dimension n so that I is a free J-module of finite rank. A sequence (f₁,...,f(n);g₁,...,g(m)) of homogeneous invariants is a Cohen-Macaulay (or CM) basis if J = K[f₁,...,f(n)] and {g₁,...,g(m)} is a basis for I as a J-module. We discuss an algorithm, and an implementation using the systems GAP and Maple, for the calculation of CM-bases.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Grove, Larry

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleComputation of polynomial invariants of finite groups.en_US
dc.creatorMcShane, Janet Marie.en_US
dc.contributor.authorMcShane, Janet Marie.en_US
dc.date.issued1992en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIf G is a finite subgroup of GL(n,K), K a field of characteristic 0, it is well known that the algebra I of polynomial invariants of G is Cohen-Macaulay. Consequently I has a subalgebra J of Krull dimension n so that I is a free J-module of finite rank. A sequence (f₁,...,f(n);g₁,...,g(m)) of homogeneous invariants is a Cohen-Macaulay (or CM) basis if J = K[f₁,...,f(n)] and {g₁,...,g(m)} is a basis for I as a J-module. We discuss an algorithm, and an implementation using the systems GAP and Maple, for the calculation of CM-bases.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairGrove, Larryen_US
dc.contributor.committeememberFan, Paulen_US
dc.contributor.committeememberGay, Daviden_US
dc.contributor.committeememberFlaschka, Hermannen_US
dc.contributor.committeememberLaetsch, Theodoreen_US
dc.identifier.proquest9307664en_US
dc.identifier.oclc713879735en_US
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