n-representation-finite algebras and n-APR tilting
By Osamu Iyama, Steffen Oppermann. 2009
133 citations recorded by the source corpus.
We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of n-APR tilting, and show that it preserves n-representation-finiteness. We give some combinatorial description of this procedure, and use this to completely describe a class of n-representation-finite algebras called "type A".
View Paper: https://www.semanticscholar.org/paper/20184bfad4927bab95d850986d1cda398746c577
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Citations in the corpus
- n-Representation infinite algebras (2012, background): “In higher dimensional AuslanderReiten theory an analogue of these algebras is given by the class of n-representation finite algebras [1, 2].”
- Silting mutation in triangulated categories (2010, background): “We note that a different generalization of ‘tilting mutation’ was given in [20, 21].”
- 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].”
- 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].”
- 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].”