J. W. MacQuarrie

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20212026

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math.RT2026

Finiteness properties of profinite blocks and blocks with defect group $Z_{p}^{n}$

Florian Eisele, John W. MacQuarrie

We prove that any block of a profinite group with a topologically finitely generated defect group $D$ is isomorphic to a block of a virtually pro- $p$ group, and if $D$ is finitely…

math.RT2025

Block pro-fusion systems for profinite groups and blocks with infinite dihedral defect groups

Florian Eisele, Ricardo J. Franquiz Flores, John W. MacQuarrie

We introduce block pro-fusion systems for blocks of profinite groups, prove a profinite version of Puig's structure theorem for nilpotent blocks, and use it to show that there is o…

math.RT2024

Projective resolutions of simple modules and Hochschild cohomology for incidence algebras

Viktor Bekkert, John William MacQuarrie, Júlio Marques

We give a practical, algorithmic method to calculate minimal projective resolutions of simple modules for a finite dimensional incidence $k$ -algebra $Λ$ , where $k$ is a field. We a…

math.RT2022

Butler's Method applied to $Z_{p} [C_{p} \times C_{p}]$ -permutation modules

John MacQuarrie, Marlon Stefano

Let $G$ be a finite $p$ -group with normal subgroup $N$ of order $p$ . The first author and Zalesskii have previously given a characterization of permutation modules for $\mathbb{Z}_…

Finiteness properties of profinite blocks and blocks with defect group Zpn​

Block pro-fusion systems for profinite groups and blocks with infinite dihedral defect groups

Projective resolutions of simple modules and Hochschild cohomology for incidence algebras

Butler's Method applied to Zp​[Cp​×Cp​]-permutation modules

Finiteness properties of profinite blocks and blocks with defect group $Z_{p}^{n}$

Butler's Method applied to $Z_{p} [C_{p} \times C_{p}]$ -permutation modules