We show that for any positive integer , there exists a quiver with vertices and edges such that any quiver on vertices is a full subquiver of a quiver mutation equivalent to . We generalize this statement to skew-symmetrizable matrices, and obtain other related results.
Revised:
Accepted:
Published online:
Keywords: Quiver mutation, universal quiver, cluster algebra.
@article{ALCO_2021__4_4_683_0, author = {Fomin, Sergey and Igusa, Kiyoshi and Lee, Kyungyong}, title = {Universal quivers}, journal = {Algebraic Combinatorics}, pages = {683--702}, publisher = {MathOA foundation}, volume = {4}, number = {4}, year = {2021}, doi = {10.5802/alco.175}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.175/} }
TY - JOUR AU - Fomin, Sergey AU - Igusa, Kiyoshi AU - Lee, Kyungyong TI - Universal quivers JO - Algebraic Combinatorics PY - 2021 SP - 683 EP - 702 VL - 4 IS - 4 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.175/ DO - 10.5802/alco.175 LA - en ID - ALCO_2021__4_4_683_0 ER -
Fomin, Sergey; Igusa, Kiyoshi; Lee, Kyungyong. Universal quivers. Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 683-702. doi : 10.5802/alco.175. http://www.numdam.org/articles/10.5802/alco.175/
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