Representations of Algebras
This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. Included are three survey articles based on short courses in the areas of commutative algebraic group...
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| Hauptverfasser: | , , |
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
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American Mathematical Society
2018
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| Ausgabe: | 1 |
| Schlagworte: | |
| ISBN: | 9781470435769, 1470435764 |
| Online-Zugang: | Volltext |
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- Appendix C. A non-finiteness assertion for tame algebras. -- References -- Noetherian properties in representation theory -- 1. Introduction -- 2. Two examples -- 3. Twisted commutative algebras -- 4. Noetherian properties -- 5. What next? -- References -- Thick tensor ideals of right bounded derived categories of commutative rings -- Introduction -- 1. Tensor triangulated categories and Balmer spectra -- 2. Compactly and cocompactly generated thick tensor ideals of \dm( ) -- 3. The Balmer spectrum of \dm( ) and classifications of thick tensor ideals -- 4. The case of discrete valuation rings and applications -- Acknowledgments -- References -- Stability, shards, and preprojective algebras -- 1. Semistable subcategories -- 2. Preprojective algebras -- 3. Weyl groups -- 4. Shards -- 5. Join-irreducibles of and bricks of Π -- 6. Technical Lemmas -- 7. Proof of Main Theorem -- 8. Connection to other work -- Acknowledgements -- References -- Computations and applications of some homological constants for polynomial representations of _{ } -- 1. Introduction -- 2. Applications of the constants ( , ) and ( , ) -- 3. Computations of ( , ) and ( , ) -- References -- Back Cover
- 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 groups -- 3. (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 algebras -- 3. 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 diagrams
- 1. 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 curve -- 2.1. 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 -- 2. Basic algebras of dimension at most 12 of blocks -- 3. Defect groups of block algebras -- 4. Some finiteness conjectures -- 5. Hochschild cohomology background -- 6. ⁰( ) -- 7. ¹( ) -- 8. Integrable derivations -- 9. Invariance properties of integrable derivations -- 10. Separably equivalent algebras -- 11. Finitistic and dominant dimensions -- 12. Fusion and algebra structure of blocks -- References -- Kronecker modules generated by modules of length 2 -- 1. Introduction -- 2. Preliminaries -- 3. The bristled modules for =1 and =2. -- 4. Proof of the main theorem. -- 5. Further considerations. -- Appendix A. The bristle variety ( ) of a Kronecker module . -- Appendix B. Bristled modules for arbitrary artin algebras.