Title Representations of Algebras

Published Providence : American Mathematical Society, 2018

Click on the following:
ProQuest Ebook Central

Copies

Description 1 online resource (294 pages) Series Contemporary Mathematics Ser. ; v. 705 Contemporary Mathematics Ser Contents 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 Summary 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 Notes 2. Basic algebras of dimension at most 12 of blocks Print version record Subject Algebra. Geometry, Algebraic -- Abelian varieties and schemes -- Isogeny.-msc Geometry, Algebraic -- Birational geometry -- McKay correspondence.-msc Associative rings and algebras -- Homological methods -- Homological dimension.-msc Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Connections with combinatorics.-msc Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings.-msc Category theory Commutative algebra -- Arithmetic rings and other special rings -- Cluster algebras.-msc Functions of a complex variable -- Riemann surfaces -- Compact Riemann surfaces and uniformization.-msc Group theory and generalizations -- Linear algebraic groups and related topics -- Cohomology theory.-msc Group theory and generalizations -- Linear algebraic groups and related topics -- Structure theory.-msc Algebra, Homological -- Abelian categories -- Localization of categories.-msc Algebra, Homological -- Categories and geometry -- Grothendieck groups.-msc Representations of algebras. Representations of groups. algebra. Algebra. Representations of algebras. Representations of groups. Algebraic geometry -- Abelian varieties and schemes -- Isogeny. Algebraic geometry -- Birational geometry -- McKay correspondence. Associative rings and algebras -- Homological methods -- Homological dimension. Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Connections with combinatorics. Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings. Category theory; homological algebra -- Categories and geometry -- Grothendieck groups. Commutative algebra -- Arithmetic rings and other special rings -- Cluster algebras. Functions of a complex variable -- Riemann surfaces -- Compact Riemann surfaces and uniformization. Group theory and generalizations -- Linear algebraic groups and related topics -- Cohomology theory. Group theory and generalizations -- Linear algebraic groups and related topics -- Structure theory. Category theory; homological algebra -- Abelian categories -- Localization of categories. Form Electronic book Author Bleher, Frauke Schiffler, Ralf ISBN 9781470447212 1470447215

  Permalink