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On the invariant theory of finite unipotent groups generated by bireflections

Horan, Katherine (2017) On the invariant theory of finite unipotent groups generated by bireflections. Doctor of Philosophy (PhD) thesis, University of Kent,. (KAR id:65736)

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Abstract

Let k be a field of characteristic p and let V be a k-vector space. In Chapter 2 of this thesis we classify all unipotent groups G ? GL(V ) consisting of bireflections for p not equal to 2: we show that unipotent groups consisting of bireflections are either two-row groups, two-column groups, hook groups or one of two types of exceptional group.

In Chapter 3 we introduce techniques and notation which we use later to find invariant rings of groups by viewing them as subgroups of Nakajima groups. In Chapter 4 we show that for k = Fp there is a family of hook groups, including all non-abelian hook groups, which have complete intersection invariant rings.

Finally in Chapter 6 we show that when k = F_p both types of exceptional group have complete intersection invariant rings.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Fleishmann, Peter
Thesis advisor: Shank, Jim
Uncontrolled keywords: Commutative Algebra Modular Invariant Theory Bireflection Bireflections Groups
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
SWORD Depositor: System Moodle
Depositing User: System Moodle
Date Deposited: 16 Jan 2018 09:10 UTC
Last Modified: 16 Feb 2021 13:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/65736 (The current URI for this page, for reference purposes)
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