On the Generalized Cluster Algebras of Geometric Type
| Autor: | Xueqing Chen, Fan Xu, Liqian Bai, Ming Ding |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Monomial
010102 general mathematics Mathematics - Rings and Algebras Type (model theory) 01 natural sciences Upper and lower bounds Cluster algebra Combinatorics Rings and Algebras (math.RA) 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Analysis Mathematics |
| Popis: | We develop and prove the analogs of some results shown in [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52] concerning lower and upper bounds of cluster algebras to the generalized cluster algebras of geometric type. We show that lower bounds coincide with upper bounds under the conditions of acyclicity and coprimality. Consequently, we obtain the standard monomial bases of these generalized cluster algebras. Moreover, in the appendix, we prove that an acyclic generalized cluster algebra is equal to the corresponding generalized upper cluster algebra without the assumption of the existence of coprimality. |
| Databáze: | OpenAIRE |
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