(Quantum) cluster algebra and quiver representation View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

2014-2016

FUNDING AMOUNT

220000 CNY

ABSTRACT

Cluster algebras and quantum cluster algebras turned out to be related to various areas in mathematics,and especially their close links with quiver representations have recently become an international hot research field. In this project,we will use quiver representations to investigate the structures of acyclic cluster algebras and quantum cluster algebras,and the main contents are described as follows: based on the work of Ding-Xiao-Xu and Geiss-Leclerc-Schr?er,we will construct the canonical bases of acyclic cluster algebras;for affine quantum cluster algebras,compute explicit expressions for the canonical triangular bases constructed by Berenstein-Zelevinsky;for acyclic quantum cluster algebras, we will study the generalized quantum cluster characters,establish the multiplication formulas of these quantum cluster algebras and construct quantum analogues of canonical bases for the corresponding cluster algebras. More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=11301282

Related SciGraph Publications

  • 2016-12. Positivity for Generalized Cluster Variables of Affine Quivers in ALGEBRAS AND REPRESENTATION THEORY
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