Cluster Monomials in Graph Laurent Phenomenon Algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912627581517824 |
|---|---|
| author | Moura, Guilherme Zeus Dantas e Kandalam, Ramanuja Charyulu Telekicherla Woodruff, Dora |
| author_facet | Moura, Guilherme Zeus Dantas e Kandalam, Ramanuja Charyulu Telekicherla Woodruff, Dora |
| contents | Laurent phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Graph Laurent phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent phenomenon algebras whose structure is given by the data of a directed graph. In this paper, we prove that the cluster monomials of a graph Laurent phenomenon algebra form a linear basis, as conjectured by Lam and Pylyavskyy and analogous to a result for cluster algebras by Caldero and Keller. We also prove that, if the graph is a bidirected tree, the coefficients of the expansion of any monomial in terms of cluster monomials are nonnegative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cluster Monomials in Graph Laurent Phenomenon Algebras Moura, Guilherme Zeus Dantas e Kandalam, Ramanuja Charyulu Telekicherla Woodruff, Dora Representation Theory Combinatorics Rings and Algebras 13F60 Laurent phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Graph Laurent phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent phenomenon algebras whose structure is given by the data of a directed graph. In this paper, we prove that the cluster monomials of a graph Laurent phenomenon algebra form a linear basis, as conjectured by Lam and Pylyavskyy and analogous to a result for cluster algebras by Caldero and Keller. We also prove that, if the graph is a bidirected tree, the coefficients of the expansion of any monomial in terms of cluster monomials are nonnegative. |
| title | Cluster Monomials in Graph Laurent Phenomenon Algebras |
| topic | Representation Theory Combinatorics Rings and Algebras 13F60 |
| url | https://arxiv.org/abs/2404.16153 |