Reddening Sequences of Infinite Quivers
Start Date
August 2025
End Date
August 2025
Location
ALT 307
Abstract
A quiver is a pair Q = (V, E) with V a set of vertices and E a multiset of arrows between two distinct vertices. Mutation is a local process of creating a new quiver from the previous. An infinite quiver Q∞ is the limit of {Qi, τi}, where Qi is an induced subquiver of Qi+1 for all i and {τi} is a sequence of embeddings. We establish a definition for mutation on an infinite quiver and demonstrate that it is well-defined. In addition, we consider reddening sequences for infinite quivers and show a constructive way to determine if an infinite quiver has such a reddening sequence.
Reddening Sequences of Infinite Quivers
ALT 307
A quiver is a pair Q = (V, E) with V a set of vertices and E a multiset of arrows between two distinct vertices. Mutation is a local process of creating a new quiver from the previous. An infinite quiver Q∞ is the limit of {Qi, τi}, where Qi is an induced subquiver of Qi+1 for all i and {τi} is a sequence of embeddings. We establish a definition for mutation on an infinite quiver and demonstrate that it is well-defined. In addition, we consider reddening sequences for infinite quivers and show a constructive way to determine if an infinite quiver has such a reddening sequence.
