An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$

Fuente: arXiv
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Main Authors: Rüping, Henrik, Stephan, Marc
Format: Preprint
Published: 2024
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author Rüping, Henrik
Stephan, Marc
author_facet Rüping, Henrik
Stephan, Marc
contents We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total homology for finite groups $Q$ of odd order. We deduce that cochain complexes of finite, free $A_4$-CW complexes with four-dimensional total homology are rigid: They are determined by the degrees of the nonzero homology groups.
format Preprint
id arxiv_https___arxiv_org_abs_2404_10735
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$
Rüping, Henrik
Stephan, Marc
Commutative Algebra
Algebraic Topology
Rings and Algebras
Primary 16E35, Secondary 55M35, 16S35, 20J05, 18G40
We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total homology for finite groups $Q$ of odd order. We deduce that cochain complexes of finite, free $A_4$-CW complexes with four-dimensional total homology are rigid: They are determined by the degrees of the nonzero homology groups.
title An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$
topic Commutative Algebra
Algebraic Topology
Rings and Algebras
Primary 16E35, Secondary 55M35, 16S35, 20J05, 18G40
url https://arxiv.org/abs/2404.10735