This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras.

Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories.

Zusammenfassung

This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras.

Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulate categories.

Inhalt
C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions.- L. Avramov : (Contravariant) Koszul duality for DG algebras.- R. Buchweitz: The fundamental group of a morphism in a triangulated category.- K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras.- D. Happel: Algebras of finite global dimension.- K. Igusa (with G. Todorov): Continuous Frobenius categories.- D.A. Jorgensen: Triangle functors from generic hypersurfaces.- Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian.- H. Krause: Morphisms determined by objects in triangulated categories.- P. Malicki (with J. A. de la Pena and A. Skowronski): Cycle-finite module categories.- J.A. de la Pena, P. Malicki and A. Skowronski: Cycle-finite module categories.- C.M. Ringel: Distinguished bases of exceptional modules.- A. Skowronski (with P. Malicki and J. A. de la Pena): Cycle-finite module categories.- D. Speyer and H. Thomas: Acyclic cluster algebras revisited.- H. Thomas and D. Speyer: Acyclic cluster algebras revisited.- G. Todorov and K. Igusa: Continuous Frobenius categories.- L. Williams and Y. Kodama: Combinatorics of KP solutions from the real Grassmannian.- D. Zacharia and D. Happel: Algebras of finite global dimension.