Mutation-equivalence in Tree-triangle Quivers
Start Date
7-8-2026 11:30 AM
End Date
7-8-2026 11:45 AM
Location
ALT 205
Abstract
Cluster algebras were first introduced by Fomin and Zelevinsky in 2001 to understand total positivity in semisimple groups by quiver mutation. Fomin poses the question of developing an algorithm that determines if two quivers are mutation-equivalent. In this paper, we build on prior research into quivers with the same underlying tree by extending the algorithm to handle graphs with 3-cycles, or triangles. We define four types of quiver triangles that determine mutation-equivalence based on their position in the tree. This algorithm provides a framework for answering Fomin’s problem for certain families of graphs.
Mutation-equivalence in Tree-triangle Quivers
ALT 205
Cluster algebras were first introduced by Fomin and Zelevinsky in 2001 to understand total positivity in semisimple groups by quiver mutation. Fomin poses the question of developing an algorithm that determines if two quivers are mutation-equivalent. In this paper, we build on prior research into quivers with the same underlying tree by extending the algorithm to handle graphs with 3-cycles, or triangles. We define four types of quiver triangles that determine mutation-equivalence based on their position in the tree. This algorithm provides a framework for answering Fomin’s problem for certain families of graphs.
