Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
Rooted mutation groups and finite type cluster algebras. |
| Συγγραφείς: |
Saleh, Ibrahim (AUTHOR) salehi@uww.edu |
| Πηγή: |
Discussiones Mathematicae: General Algebra & Applications. 2025, Vol. 45 Issue 2, p261-279. 19p. |
| Θεματικοί όροι: |
*Cluster algebras, *Mutations (Algebra), *Isomorphism (Mathematics) |
| Περίληψη: |
For a fixed seed $(X, Q)$, a rooted mutation loop is a sequence of mutations that preserves $(X, Q)$. The group generated by all rooted mutation loops is called rooted mutation group and will be denoted by $\mathcal{M}(Q)$. The global mutation group of $(X, Q)$, denoted $\mathcal{M}$, is the group of all mutation sequences subject to the relations on the cluster structure of $(X, Q)$. In this article, we show that two finite type cluster algebras $\mathcal{A}(Q)$ and $\mathcal{A}(Q')$ are isomorphic if and only if their rooted mutation groups are isomorphic and the sets $\mathcal{M}/\mathcal{M}(Q)$ and $\mathcal{M'}/\mathcal{M}(Q')$ are in one to one correspondence. The second main result shows that the group $\mathcal{M}(Q)$ and the set $\mathcal{M}/\mathcal{M}(Q)$ determine the finiteness of the cluster algebra $\mathcal{A}(Q)$ and vice versa. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
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