Periodic Algebras which are Almost Koszul

By S. Brenner, M. C. R. Butler, A. King. 2002

144 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3850960d74bfc1f48f3c1431ea210b0ee17afa46

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Bernard Leclerc
2. C. Geiss
3. J. Schröer
4. Yuya Mizuno
5. V. Ginzburg
6. Osamu Iyama
7. Pavel Etingof
8. Gustavo Jasso

In Geometry and Topology

1. Osamu Iyama
2. Bernard Leclerc
3. B. Keller
4. C. Geiss
5. Yuya Mizuno
6. J. Schröer
7. I. Reiten
8. V. Ginzburg

In Statistical and Nonlinear Physics

1. V. Ginzburg
2. Gustavo Jasso
3. Pavel Etingof
4. C. Geiss
5. J. Schröer
6. Bernard Leclerc
7. Travis Schedler
8. Ching-Hwa Eu

Citations in the corpus

• Calabi-Yau Frobenius algebras (2007, result): “t is proved that ΠTn is periodic Calabi-Yau Frobenius of dimension 5 (and shift h+ 2) and period 6 (and shift 2h). Also, in [Eu], a correction to results of [ES98a] in type Ais given. Example 2.4.14. [BBK02] The trivial extension algebras of path algebras of Dynkin quivers are periodic Calabi-Yau Fr”
• Stability conditions and Kleinian singularities (2005, background): “These two actions commute, and the action of the shift functor [1] coincides with the action of 1 ∈ C.”
• Classifying tilting complexes over preprojective algebras of Dynkin type (2015, background): “MR Zbl [Brenner et al. 2002] S. Brenner, M. C. R. Butler, and A. D. King, “Periodic algebras which are almost Koszul”, Algebr.”
• Higher Nakayama algebras I: Construction (2016, background): “d new examples of d-abelian and (d+ 2)-angulated categories in the sense of [Jas16] and [GKO13] respectively. In a forthcoming article [JK16] we establish the (almost) Koszul property in the sense of [BBK02] and the Calabi{Yau property in the sense of [Gin06] of certain higher Nakayama algebras. By ”
• Classifying $$\tau $$τ-tilting modules over preprojective algebras of Dynkin type (2013, background): “We refer to [7,12,17,34] for basic properties and background information.”
• Semicanonical bases and preprojective algebras II: A multiplication formula (2005, background): “It follows for example from the proof of [ 3, Theorem 3.15 ].”
• Noncommutative geometry and quiver algebras (2005, background): “ L). 8.5 Dynkin case. In the case of (finite) Dynkin quiver Q, the corresponding preprojective algebra Π is not Koszul, in general, and there are nonzero cohomology groups HHi(Π) for i>2, see [ES], [BBK]. Now let Qbe an extended Dynkin quiver and let Γ ⊂ SL2(k) be the finite group associated to Qvi”