DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type L n (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane...
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| Format: | Journal article |
| Language: | English |
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2012
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| _version_ | 1797098948457922560 |
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| author | Bialkowski, J Erdmann, K Skowronski, A |
| author_facet | Bialkowski, J Erdmann, K Skowronski, A |
| author_sort | Bialkowski, J |
| collection | OXFORD |
| description | In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type L n (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type A 2n. In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂ n are isomorphic to the canonical mesh algebras of type ℂ n, and hence to the stable Auslander algebras of simple plane curve singularities of type A 2n-1. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂ n. © Instytut Matematyczny PAN, 2012. |
| first_indexed | 2024-03-07T05:16:48Z |
| format | Journal article |
| id | oxford-uuid:dd7d9fb8-3a52-4b00-937e-ae7b89abc173 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:16:48Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:dd7d9fb8-3a52-4b00-937e-ae7b89abc1732022-03-27T09:25:28ZDEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-nJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:dd7d9fb8-3a52-4b00-937e-ae7b89abc173EnglishSymplectic Elements at Oxford2012Bialkowski, JErdmann, KSkowronski, AIn our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type L n (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type A 2n. In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂ n are isomorphic to the canonical mesh algebras of type ℂ n, and hence to the stable Auslander algebras of simple plane curve singularities of type A 2n-1. Moreover, we describe the minimal (periodic) bimodule projective resolutions of the canonical mesh algebras of type ℂ n. © Instytut Matematyczny PAN, 2012. |
| spellingShingle | Bialkowski, J Erdmann, K Skowronski, A DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title | DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title_full | DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title_fullStr | DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title_full_unstemmed | DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title_short | DEFORMED MESH ALGEBRAS OF DYNKIN TYPE C-n |
| title_sort | deformed mesh algebras of dynkin type c n |
| work_keys_str_mv | AT bialkowskij deformedmeshalgebrasofdynkintypecn AT erdmannk deformedmeshalgebrasofdynkintypecn AT skowronskia deformedmeshalgebrasofdynkintypecn |