Quivers with potentials associated with triangulations of Riemann surfaces

Title:
Quivers with potentials associated with triangulations of Riemann surfaces
Creator:
Labardini-Fragoso, Daniel (Author)
Contributor:
Zelevinsky, Andrei V. (Advisor)
Weyman, Jerzy M. (Committee member)
Todorov, Gordana G. (Committee member)
Derksen, Harm (Committee member)
Publisher:
Boston, Massachusetts : Northeastern University, 2010
Date Accepted:
December 2010
Date Awarded:
May 2011
Type of resource:
Text
Genre:
Dissertations
Format:
electronic
Digital origin:
born digital
Abstract/Description:
We study the behavior of quivers with potentials and their mutations introduced by Derksen-Weyman-Zelevinsky in the combinatorial framework developed by Fomin-Shapiro-Thurston for cluster algebras that arise from bordered Riemann surfaces with marked points.

In Part I we associate to each ideal triangulation of a bordered surface with marked points a quiver with potential, in such a way that whenever two ideal triangulations are related by a flip of an arc, the respective quivers with potentials are related by a mutation with respect to the flipped arc. We prove that if the surface has non-empty boundary, then the quivers with potentials associated to its triangulations are rigid and hence non-degenerate, and have finite-dimensional Jacobian algebra.

In Part II we define, given an arc and an ideal triangulation of a bordered marked surface, a representation of the quiver with potential constructed in Part I, so that whenever two ideal triangulations are related by a flip, the associated representations are related by the corresponding mutation of representations.
Subjects and keywords:
theoretical mathematics
flip
mutation
potential
quiver
representation
triangulation
Mathematics
DOI:
https://doi.org/10.17760/d20000727
Permanent Link:
http://hdl.handle.net/2047/d20000727
Use and reproduction:
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