Matrices as graded BiHom-algebras and decompositions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918008788615168 |
|---|---|
| author | Sun, Jiacheng Wang, Shuanhong Zhu, Haoran |
| author_facet | Sun, Jiacheng Wang, Shuanhong Zhu, Haoran |
| contents | We present matrices as graded BiHom-algebras and consider various characteristics of their decompositions. Specifically, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded ideals. We show that, under suitable assumptions, such as $Σ$-multiplicativity, maximal length, and centre triviality, the matrix BiHom-algebra decomposes into a direct sum of graded simple ideals. We further extend our results to general graded BiHom-algebras over arbitrary base fields. As applications, we reinterpret classical gradings on matrix algebras such as those induced by Pauli matrices and the $\mathbb{Z}_n \times \mathbb{Z}_n $-grading in terms of our setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrices as graded BiHom-algebras and decompositions Sun, Jiacheng Wang, Shuanhong Zhu, Haoran Rings and Algebras Quantum Algebra We present matrices as graded BiHom-algebras and consider various characteristics of their decompositions. Specifically, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded ideals. We show that, under suitable assumptions, such as $Σ$-multiplicativity, maximal length, and centre triviality, the matrix BiHom-algebra decomposes into a direct sum of graded simple ideals. We further extend our results to general graded BiHom-algebras over arbitrary base fields. As applications, we reinterpret classical gradings on matrix algebras such as those induced by Pauli matrices and the $\mathbb{Z}_n \times \mathbb{Z}_n $-grading in terms of our setting. |
| title | Matrices as graded BiHom-algebras and decompositions |
| topic | Rings and Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2505.02191 |