Mutating seeds: types $𝔸$ and $\stackrel{˜}{𝔸}$.
Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 29-73.

In the cases $𝔸$ and $\stackrel{˜}{𝔸}$, we describe the seeds obtained by sequences of mutations from an initial seed. In the $\stackrel{˜}{𝔸}$ case, we deduce a linear representation of the group of mutations which contains as matrix entries all cluster variables obtained after an arbitrary sequence of mutations (this sequence is an element of the group). Nontransjective variables correspond to certain subgroups of finite index. A noncommutative rational series is constructed, which contains all this information.

DOI : https://doi.org/10.5802/ambp.304
Classification : 13F60,  16G20,  16G99
Mots clés: Cluster algebras, mutations, seeds, quivers
@article{AMBP_2012__19_1_29_0,
author = {Ibrahim Assem and Christophe Reutenauer},
title = {Mutating seeds: types $\mathbb{A}$ and $\widetilde{\mathbb{A}}$.},
journal = {Annales Math\'ematiques Blaise Pascal},
pages = {29--73},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {19},
number = {1},
year = {2012},
doi = {10.5802/ambp.304},
mrnumber = {2978313},
zbl = {1259.13013},
language = {en},
url = {ambp.centre-mersenne.org/item/AMBP_2012__19_1_29_0/}
}
Ibrahim Assem; Christophe Reutenauer. Mutating seeds: types $\mathbb{A}$ and $\widetilde{\mathbb{A}}$.. Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 29-73. doi : 10.5802/ambp.304. https://ambp.centre-mersenne.org/item/AMBP_2012__19_1_29_0/

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