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Atomic bases of cluster algebras of types A and Ã
Author(s) -
Dupont Grégoire,
Thomas Hugh
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdt001
Subject(s) - mathematics , cluster algebra , cluster (spacecraft) , semiring , basis (linear algebra) , pure mathematics , type (biology) , algebra over a field , combinatorics , quantum , physics , quantum mechanics , geometry , computer science , ecology , biology , programming language
We give explicit atomic bases of arbitrary coefficient‐free cluster algebras of types A and à . This entails showing that the minimal elements of the positive semiring of these cluster algebras form a linear basis over the integers for the cluster algebra.