Support varieties for selfinjective algebras
Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results fr...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797101351645216768 |
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| author | Erdmann, K Holloway, M Snashall, N Solberg, O Taillefer, R |
| author_facet | Erdmann, K Holloway, M Snashall, N Solberg, O Taillefer, R |
| author_sort | Erdmann, K |
| collection | OXFORD |
| description | Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true. |
| first_indexed | 2024-03-07T05:50:39Z |
| format | Journal article |
| id | oxford-uuid:e8c4c4f8-4b2b-4df4-9b54-3b756d8724da |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:50:39Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:e8c4c4f8-4b2b-4df4-9b54-3b756d8724da2022-03-27T10:49:11ZSupport varieties for selfinjective algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e8c4c4f8-4b2b-4df4-9b54-3b756d8724daEnglishSymplectic Elements at Oxford2003Erdmann, KHolloway, MSnashall, NSolberg, OTaillefer, RSupport varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true. |
| spellingShingle | Erdmann, K Holloway, M Snashall, N Solberg, O Taillefer, R Support varieties for selfinjective algebras |
| title | Support varieties for selfinjective algebras |
| title_full | Support varieties for selfinjective algebras |
| title_fullStr | Support varieties for selfinjective algebras |
| title_full_unstemmed | Support varieties for selfinjective algebras |
| title_short | Support varieties for selfinjective algebras |
| title_sort | support varieties for selfinjective algebras |
| work_keys_str_mv | AT erdmannk supportvarietiesforselfinjectivealgebras AT hollowaym supportvarietiesforselfinjectivealgebras AT snashalln supportvarietiesforselfinjectivealgebras AT solbergo supportvarietiesforselfinjectivealgebras AT tailleferr supportvarietiesforselfinjectivealgebras |