Cluster complexes via semi-invariants
By Kiyoshi Igusa, K. Orr, G. Todorov, Jerzy Weyman. Compositio Mathematica, 2007
53 citations recorded by the source corpus.
Abstract We define and study virtual representation spaces for vectors having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual semi-invariants and prove that they satisfy the three basic theorems: the first fundamental theorem, the saturation theorem and the canonical decomposition theorem. In the special case of Dynkin quivers with n vertices, this gives the fundamental interrelationship between supports of the semi-invariants and the tilting triangulation of the (n−1)-sphere.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1a885d8455c5cb560314fc05d51fe1fe5a68287b
How researchers see this paper
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In Discrete Mathematics and Combinatorics
- Laurent Demonet
- Thomas Brustle
- B. Keller
- H. Treffinger
- Harm Derksen
- David Andrew Smith
- S. Cecotti
- C. Vafa
In Geometry and Topology
- Laurent Demonet
- B. Keller
- Thomas Brustle
- Harm Derksen
- J. Fei
- H. Treffinger
- David Andrew Smith
- Osamu Iyama
In Mathematical Physics
- Thomas Brustle
- Laurent Demonet
- Harm Derksen
- J. Fei
- B. Keller
- H. Treffinger
- David Andrew Smith
- Alexander Kuznetsov
Citations in the corpus
- Noncrossing partitions and the shard intersection order (2009, unknown): “Ψ/Θc and the domains of virtual semi-invariants considered in [20].”
- Wall and chamber structure for finite-dimensional algebras (2018, background): “Since then, the study of rings of quiver semi-invariants by Derksen and Weyman [17] has been expanded to the context of cluster algebras.”
- A survey on maximal green sequences (2019, background): “Other topics closely related to the representationtheoretic proof are the investigation of chains of torsion classes induced by stability conditions [64, 63, 14, 4, 13, 109], the wall and chamber structure of the space of stability conditions [15] and the study of semi-invariants and picture groups ”
- General Presentations of Algebras (2009, background): “Similar questions for general presentations of path algebras without relations were studied in [13] through a different approach.”