تقرير
Factoriality and class groups of cluster algebras
| العنوان: | Factoriality and class groups of cluster algebras |
|---|---|
| المؤلفون: | Elsener, Ana Garcia, Lampe, Philipp, Smertnig, Daniel |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Commutative Algebra, Mathematics - Rings and Algebras, 13F60 (Primary) 13A15, 13F05, 13F15 (Secondary) |
| الوصف: | Locally acyclic cluster algebras are Krull domains. Hence their factorization theory is determined by their (divisor) class group and the set of classes containing height-1 prime ideals. Motivated by this, we investigate class groups of cluster algebras. We show that any cluster algebra that is a Krull domain has a finitely generated free abelian class group, and that every class contains infinitely many height-$1$ prime ideals. For a cluster algebra associated to an acyclic seed, we give an explicit description of the class group in terms of the initial exchange matrix. As a corollary, we reprove and extend a classification of factoriality for cluster algebras of Dynkin type. In the acyclic case, we prove the sufficiency of necessary conditions for factoriality given by Geiss--Leclerc--Schr\"oer. Comment: 35 pages; significant revision (numbering of main theorems has changed; added section 7) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1712.06512 |
| رقم الأكسشن: | edsarx.1712.06512 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |