Quiver-graded Richardson orbits

Eiriksson, Ögmundur; Sauter, Julia

doi:10.1080/00927872.2019.1588974

Cited by 2 publications

(3 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 6.14. We remark again that the nilpotent quiver algebra defined here is the opposite algebra of the nilpotent quiver algebra defined by Eiriksson and Sauter in [ES17], however the effect on the quasi-hereditary structure is straightforward as is explained in Remark 6.4.…”

Section: Applications and Examplesmentioning

confidence: 81%

“…We also prove that when Q has no sinks the ADR algebra coincides with the quiver nilpotent algebra N m (Q) introduced by Eiriksson and Sauter [ES17], which is motivated via a quiver graded version of Richardson orbits and is recapped in Section 6.4.…”

mentioning

confidence: 86%

“…It follows from [ES17,Proposition 3.15] that all nilpotent quiver algebras N s (Q) are right strongly quasi-hereditary and left ultra strongly quasi-hereditary for the quasihereditary structure determined by the layer function L(i t ) = s − t.…”

Section: Applications and Examplesmentioning

confidence: 99%

See 2 more Smart Citations

Ringel duality for certain strongly quasi-hereditary algebras

Kalck¹,

Karmazyn

2018

European Journal of Mathematics

View full text Add to dashboard Cite

We study quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary algebras.As special cases, we obtain a Ringel-duality formula for a family of strongly quasihereditary algebras arising from a type A configuration of projective lines in a rational, projective surface as recently introduced by Hille and Ploog, for certain Auslander-Dlab-Ringel algebras, and for Eiriksson and Sauter's nilpotent quiver algebras when the quiver has no sinks and no sources. We also recover Tan's result that the Auslander algebras of self-injective Nakayama algebras are Ringel self-dual. Ringel duality [Rin91] is a fundamental phenomenon in the theory of quasi-hereditary algebras, see for example [Kra13,GGOR03,BK17,CM17,Puč15,IR11,EP04,CE17,Cou17] for (recent) work on this topic. For any quasi-hereditary algebra A there exists a quasihereditary algebra R(A), the Ringel-dual of A, such that A-mod ∼ = R(R(A))-mod.

show abstract

Section: Applications and Examplesmentioning

confidence: 81%

mentioning

confidence: 86%

See 1 more Smart Citation

Ringel duality for certain strongly quasi-hereditary algebras

Kalck¹,

Karmazyn

2018

European Journal of Mathematics

View full text Add to dashboard Cite

show abstract

On Quiver Grassmannians and Orbit Closures for Gen-Finite Modules

Pressland

Sauter

2021

Algebr Represent Theor

Self Cite

View full text Add to dashboard Cite

We show that endomorphism rings of cogenerators in the module category of a finite-dimensional algebra A admit a canonical tilting module, whose tilted algebra B is related to A by a recollement. Let M be a gen-finite A-module, meaning there are only finitely many indecomposable modules generated by M. Using the canonical tilts of endomorphism algebras of suitable cogenerators associated to M, and the resulting recollements, we construct desingularisations of the orbit closure and quiver Grassmannians of M, thus generalising all results from previous work of Crawley-Boevey and the second author in 2017. We provide dual versions of the key results, in order to also treat cogen-finite modules.

show abstract

Quiver-graded Richardson orbits

Cited by 2 publications

References 32 publications

Ringel duality for certain strongly quasi-hereditary algebras

Ringel duality for certain strongly quasi-hereditary algebras

On Quiver Grassmannians and Orbit Closures for Gen-Finite Modules

Contact Info

Product

Resources

About