Basics on positively multiplicative graphs and algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866910841251561472 |
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| author | Guilhot, Jérémie Lecouvey, Cédric Tarrago, Pierre |
| author_facet | Guilhot, Jérémie Lecouvey, Cédric Tarrago, Pierre |
| contents | An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with $A$. The goal of this paper is to present basic properties of this notion and explain, through various simple examples, how it relates to highly non trivial problems like the combinatorial description of fusion rules, the description of the minimal boundary of graded graphs or the study of random walks on alcove tilings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08889 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Basics on positively multiplicative graphs and algebras Guilhot, Jérémie Lecouvey, Cédric Tarrago, Pierre Combinatorics Commutative Algebra Representation Theory An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with $A$. The goal of this paper is to present basic properties of this notion and explain, through various simple examples, how it relates to highly non trivial problems like the combinatorial description of fusion rules, the description of the minimal boundary of graded graphs or the study of random walks on alcove tilings. |
| title | Basics on positively multiplicative graphs and algebras |
| topic | Combinatorics Commutative Algebra Representation Theory |
| url | https://arxiv.org/abs/2205.08889 |