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Grassmannians and Cluster Structures
Cluster structures have been established on numerous algebraic varieties. These lectures focus on the Grassmannian variety and explain the cluster...
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Tilting Modules and Exceptional Sequences for a Family of Dual Extension Algebras
We provide a classification of generalized tilting modules and full exceptional sequences for a certain family of quasi-hereditary algebras, namely...
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Degenerate Affine Flag Varieties and Quiver Grassmannians
We study finite dimensional approximations to degenerate versions of affine flag varieties using quiver Grassmannians for cyclic quivers. We prove...
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Dualities from iterated tilting
First a duality theory is developed for arbitrary finite-dimensional algebras Λ and Λ′. It provides a characterization of the contravariant...
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On String Algebras and the Cohen–Macaulay Auslander Algebras
The Cohen–Macaulay Auslander algebra of an algebra A is defined as the endomorphism algebra of the direct sum of all indecomposable Gorenstein...
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Non-Commutative Resolutions for the Discriminant of the Complex Reflection Group G(m, p, 2)
We show that for the family of complex reflection groups G = G ( m , p ,2) appearing in the Shephard–Todd classification, the endomorphism ring of the...
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On simple-minded systems over domestic Brauer graph algebras
Let A be a domestic Brauer graph algebra over an algebraically closed field. We present a practical criterion for an orthogonal system in the stable...
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A note on stable equivalences of finite dimensional algebras
Here, we will show that, under mild conditions, stable equivalences preserve Gorenstein global dimension, CM-freeness, CM-finiteness,...
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Spectral Methods in Representation Theory
This chapter deals with the Coxeter transformation associated with the Cartan matrix of a basic algebra. We relate Coxeter spectral properties to the...
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Auslander–Reiten quiver and representation theories related to KLR-type Schur–Weyl duality
We introduce new partial orders on the sequence positive roots and study the statistics of the poset by using Auslander–Reiten quivers for finite...
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Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams
To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with...
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Constructing almost split sequences
The previous chapter was mainly of a theoretical nature: we defined irreducible morphisms and almost split sequences and started to explore their use...
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Low dimensional orders of finite representation type
In this paper, we study noncommutative surface singularities arising from orders. The singularities we study are mild in the sense that they have...
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On Simple-Minded Systems Over Representation-Finite Self-Injective Algebras
Let A be a representation-finite self-injective algebra over an algebraically closed field k . We give a new characterization for an orthogonal system...
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Differential Projective Modules Over Algebras with Radical Square Zero
Let Q be a finite connected quiver and Λ be the radical square zero algebra of Q . We give a bijection between the reduced differential projective...