Hybrid algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916081634902016 |
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| author | Erdmann, Karin Skowroński, Andrzej |
| author_facet | Erdmann, Karin Skowroński, Andrzej |
| contents | We introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely the blocks of idempotent algebras of weighted surface algebras, up to socle deformations. More generally, for tame symmetric algebras whose Gabriel quiver is 2-regular, we show that the tree class of an Auslander-Reiten component is Dynkin or Euclidean or one of the infinite tress $A_{\infty}$, $A_{\infty}^{\infty}$, or $D_{\infty}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_05963 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Hybrid algebras Erdmann, Karin Skowroński, Andrzej Representation Theory 16D50, 16E30, 16G20, 16G60, 16G70 We introduce a new class of symmetric algebras, which we call hybrid algebras. This class contains on one extreme Brauer graph algebras, and on the other extreme general weighted surface algebras. We show that hybrid algebras are precisely the blocks of idempotent algebras of weighted surface algebras, up to socle deformations. More generally, for tame symmetric algebras whose Gabriel quiver is 2-regular, we show that the tree class of an Auslander-Reiten component is Dynkin or Euclidean or one of the infinite tress $A_{\infty}$, $A_{\infty}^{\infty}$, or $D_{\infty}$. |
| title | Hybrid algebras |
| topic | Representation Theory 16D50, 16E30, 16G20, 16G60, 16G70 |
| url | https://arxiv.org/abs/2103.05963 |