An equivariant BGG correspondence and perfect complexes for extensions by $\mathbb{Z}/2\times \mathbb{Z}/2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911842227453952 |
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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 |
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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 |