Representations of algebras

Content: Cover
Title page
Contents
Preface
Commutative algebraic groups up to isogeny. II
1. Introduction
2. A construction of hereditary categories
2.1. Two preliminary results
2.2. Torsion pairs
2.3. The category of extensions
2.4. Universal extensions
2.5. Relation to module categories
3. Applications to commutative algebraic groups
3.1. Some isogeny categories
3.2. More isogeny categories
3.3. Functors of points
3.4. Finiteness conditions for Hom and Ext groups
3.5. Finiteness representation type: an example
References
Noncommutative resolutions of discriminants
1. Introduction. 2. Reflection groups3. (Noncommutative) resolutions of singularities
4. The classical McKay correspondence
5. NCRs of discriminants
6. Further questions
7. Acknowledgements
References
Polyhedral models for tensor product multiplicities
Introduction
1. Graded Upper Cluster Algebras
2. Auslander-Reiten theory of Presentations
3. Cluster Character from Quiver with Potential
4. iARt QPs
5. Remarks on Non-simply Laced Cases
Acknowledgment
References
Special multiserial algebras, Brauer configuration algebras and more: A survey
1. Introduction. 2. Multiserial and special multiserial algebras3. Algebras defined by cycles
4. Brauer configurations and Brauer configuration algebras
5. Connection results
6. Examples
7. Almost gentle algebras
8. Representations of multiserial algebras
9. Radical cubed zero
References
Nakayama-type phenomena in higher Auslander-Reiten theory
1. Introduction
2. Preliminaries
3. Higher Nakayama algebras
4. Obstructions to an alternative definition of higher Nakayama algebras
5. Cluster categories of type _{ } and _{∞}
References K-polynomials of type A quiver orbit closures and lacing diagrams1. Background and context
2. Lacing diagrams
3. K-polynomials of quiver orbit closures
4. The component formula
5. Open problems
References
Krull-Gabriel dimension and the Ziegler spectrum
1. Purity in categories of modules
2. The Krull-Gabriel dimension of ℛ
3. Examples
References
On the K-theory of weighted projective curves
Introduction
1. Coherent sheaves on a smooth projective curve
1.1. The Euler form
1.2. Shift action associated to a point
1.3. The divisor sequence 2. Coherent sheaves on a weighted projective curve2.1. The category of -cycles
2.2. The reduced (or numerical) Grothendieck group
2.3. Attaching tubes
2.4. Orbifold Euler characteristic and weighted Riemann-Roch
2.5. Impact of the Euler characteristic
2.6. Shift action, weighted divisor group and weighted Picard group
2.7. The localization sequence
Appendix A. Multiplicative structure
Acknowledgements
References
Finite-dimensional algebras arising as blocks of finite group algebras
Introduction
1. Properties of blocks of finite group algebras.