Selfinjective quivers with potential and 2-representation-finite algebras
By Martin Herschend, Osamu Iyama. Compositio Mathematica, 2010
80 citations recorded by the source corpus.
Abstract We study quivers with potential (QPs) whose Jacobian algebras are finite-dimensional selfinjective. They are an analogue of the ‘good QPs’ studied by Bocklandt whose Jacobian algebras are 3-Calabi–Yau. We show that 2-representation-finite algebras are truncated Jacobian algebras of selfinjective QPs, which are factor algebras of Jacobian algebras by certain sets of arrows called cuts. We show that selfinjectivity of QPs is preserved under iterated mutation with respect to orbits of the Nakayama permutation. We give a sufficient condition for all truncated Jacobian algebras of a fixed QP to be derived equivalent. We introduce planar QPs which provide us with a rich source of selfinjective QPs.
Subfields: Atomic and Molecular Physics, and Optics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d50921e93b022afb8af97551671ea35114eba12d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Discrete Mathematics and Combinatorics
- Gustavo Jasso
- Peter Jørgensen
- Osamu Iyama
- Oyvind Solberg
- Sondre Kvamme
- Lidia Angeleri Hugel
- Thomas Brustle
- B. Keller
In Geometry and Topology
- Gustavo Jasso
- Peter Jørgensen
- Sondre Kvamme
- Oyvind Solberg
- Osamu Iyama
- Lidia Angeleri Hugel
- B. Keller
- J. Št’ovíček
Citations in the corpus
- n-Abelian and n-exact categories (2014, methodology): “A distinguished class of such algebras, the socalled n-representation-finite algebras, were introduced by Iyama-Oppermann in [31] and have been studied in greater detail by Herschend-Iyama in the case n = 2, see [25].”
- An introduction to higher Auslander–Reiten theory (2016, background): “In addition to representation theory [15, 23, 31], it has exhibited connections to commutative algebra, commutative and non-commutative algebraic geometry, and combinatorics, see for example [1, 16, 17, 24, 32].”
- Torsion Classes and t-Structures in Higher Homological Algebra (2014, background): “There are rich examples of n-cluster tilting subcategories, many with interesting links to combinatorics and geometry, see [8], [9], [13], [17].”
- Auslander-Gorenstein algebras and precluster tilting (2016, result): “(We do not assume gldimΛ ≤ n in this paper in contrast with several earlier papers [18, 24, 25].”