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On the Invariant Rings of Modular Bireflection Groups with Applications of Macaulay's Double Annihilator Correspondence

Lee, Christopher (2019) On the Invariant Rings of Modular Bireflection Groups with Applications of Macaulay's Double Annihilator Correspondence. Doctor of Philosophy (PhD) thesis, University of Kent,. (KAR id:79961)

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Abstract

Let V be a faithful finite-dimensional representation of a finite group G over an odd prime field k, and S = k[V], the symmetric algebra on the dual V*. Chapter 2 shows how to find the invariant ring S^G when G is an abelian unipotent two-row group. The invariant rings are complete intersections.

Chapter 3 shows an algorithm that computes the Macaulay inverse for any homogenous (S^+)-primary irreducible ideal of S. It will also be shown that the Hilbert ideal of the invariant rings of the abelian two-row groups from chapter 2 are complete intersection ideals with inverse monomials as Macaulay inverses.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Fleischmann, Peter
Thesis advisor: Shank, Jim
Thesis advisor: Pech, Clelia
Uncontrolled keywords: Modular Invariant Theory Abelian Two-Row Groups
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Organisations -1 not found.
SWORD Depositor: System Moodle
Depositing User: System Moodle
Date Deposited: 05 Feb 2020 12:10 UTC
Last Modified: 19 Dec 2022 19:31 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/79961 (The current URI for this page, for reference purposes)
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