Infinitesimal semi-invariant pictures and co-amalgamation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910572226805760 |
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| author | Hanson, Eric J. Igusa, Kiyoshi Kim, Moses Todorov, Gordana |
| author_facet | Hanson, Eric J. Igusa, Kiyoshi Kim, Moses Todorov, Gordana |
| contents | The purpose of this paper is to study the local structure of the semi-invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co-amalgamation, we show that this local structure is completely described by the semi-invariant pictures of a collection of self-injective Nakayama algebras. We then describe the cones of this local structure using cluster-like structures that we call support regular clusters. Finally, we show that the local structure is (piecewise linearly) invariant under cluster tilting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_06572 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Infinitesimal semi-invariant pictures and co-amalgamation Hanson, Eric J. Igusa, Kiyoshi Kim, Moses Todorov, Gordana Representation Theory Combinatorics Rings and Algebras 16G20 The purpose of this paper is to study the local structure of the semi-invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co-amalgamation, we show that this local structure is completely described by the semi-invariant pictures of a collection of self-injective Nakayama algebras. We then describe the cones of this local structure using cluster-like structures that we call support regular clusters. Finally, we show that the local structure is (piecewise linearly) invariant under cluster tilting. |
| title | Infinitesimal semi-invariant pictures and co-amalgamation |
| topic | Representation Theory Combinatorics Rings and Algebras 16G20 |
| url | https://arxiv.org/abs/2012.06572 |