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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2018
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| Abstract | 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 groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras. |
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| AbstractList | 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 groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras. |
| Author | Schiffler, Ralf Bleher, Frauke Leuschke, Graham J |
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| SubjectTerms | Abelian categories Abelian varieties and schemes Algebra-Congresses Algebraic geometry Arithmetic rings and other special rings Associative rings and algebras Birational geometry Categories and geometry Category theory Cluster algebras.-msc Cohomology theory.-msc Commutative algebra Compact Riemann surfaces and uniformization.-msc Connections with combinatorics.-msc Functions of a complex variable Grothendieck groups.-msc Group theory and generalizations homological algebra Homological dimension.-msc Homological methods Hopf algebras, quantum groups and related topics Isogeny.-msc Linear algebraic groups and related topics Localization of categories.-msc McKay correspondence.-msc Representation theory of rings and algebras Representations of algebras-Congresses Representations of Artinian rings.-msc Representations of groups-Congresses Riemann surfaces Structure theory.-msc |
| TableOfContents | 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. |
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