Representations of Algebras, Geometry and Physics

• Autore: Igusa Kiyoshi
• Pubblicazione: Providence : , : American Mathematical Society, , 2021; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (252 pages)
• Disciplina: 512/.22
• Soggetto topico: Representations of algebras; Geometry, Algebraic; Commutative algebra; Commutative algebra -- Theory of modules and ideals -- Dimension theory, depth, related rings (catenary, etc.); Algebraic geometry -- Foundations -- Generalizations (algebraic spaces, stacks); Associative rings and algebras {For the commutative case, see 13-XX} -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets; Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for; Group theory and generalizations -- Special aspects of infinite or finite groups -- Reflection and Coxeter groups [See also 22E40, 51F15]
• Classificazione: 13C1514A2016G2018D5018E1018E1518E3018F9918G5520F55
• Altri autori: MartsinkovskyAlex TodorovGordana
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Cover -- Title page -- Contents -- Preface -- Examples of geodesic ghor algebras on hyperbolic surfaces -- 1. Introduction -- 2. Ghor algebras: Background and main results -- 3. Examples -- References -- Feynman categories and representation theory -- Introduction -- 1. Representations from a categorical viewpoint -- 2. Feynman categories -- 3. Constructions and examples -- 4. Modules and enriched Feynman categories -- 5. Bar, co-bar, Feynman transforms, & -- master equations -- 6. W-construction and cubical structures -- 7. Outlook -- Appendix A. Graph glossary and graphical Feynman categories -- Appendix B. Graph description of ⁺, ^{+ } and ^{ } -- Appendix C. Double categories, 2-categories and monoidal categories -- Appendix D. Model structures -- Acknowledgments -- References -- Preprojective roots and graph monoids of Coxeter groups -- Introduction -- 1. Graph monoid -- 2. Preprojective roots -- 3. Preprojective roots and finite Coxeter groups -- 4. Reduced -admissible words -- References -- Approximable triangulated categories -- 1. Introduction -- 2. Background -- 3. Approximability-the intuition, which comes from ( ) -- 4. Measuring the complexity of an object -- 5. The formal definition of approximability -- 6. The main theorems -- 7. More about the strong generation of \dperf and ^{ }_{ }( ) -- 8. More about finite -linear functors :\big[\dperf \big]^{ }⟶\Mod and ̃ : ^{ }_{ }( )⟶\Mod -- 9. The categories \dperf and ^{ }_{ }( ) determine each other -- Appendix A. Some dumb maps in _{}ℭ^{ℭ'}( ), and the proof that the third map of the triangle is a cochain map -- Appendix B. The assumption that the short exact sequences of cochain complexes are degreewise split is harmless -- Appendix C. Translating the approach to derived categories we presented here to the more standard one in the literature. ; Acknowledgments -- References -- Methods of constructive category theory -- Introduction -- 1. Category constructors -- 1.1. Computable categories -- 1.2. \Ab-categories -- 1.3. Additive closure -- 1.4. Homomorphism structures -- 1.5. Freyd category -- 1.6. Computing with Freyd categories -- 1.6.1. Equality of morphisms -- 1.6.2. Cokernels -- 1.6.3. Kernels -- 1.6.4. The abelian case -- 1.6.5. Homomorphisms -- 1.7. Computing natural transformations -- 2. Constructive diagram chases -- 2.1. Additive relations -- 2.2. Category of generalized morphisms -- 2.3. Computation rules -- 2.4. Cohomology -- 2.5. Snake lemma -- 2.6. Generalized homomorphism theorem -- 2.7. Computing spectral sequences -- References -- The HRS tilting process and Grothendieck hearts of t-structures -- 1. Introduction -- 2. Preliminaries -- 3. Projective and injective objects in the heart. Quasi-(co)tilting torsion pairs -- 4. When is the heart of a torsion pair a Grothendieck category? -- 5. Beyond the HRS case: Some recent results -- Acknowledgments -- References -- Back Cover.
• Sommario/riassunto: This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA.Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called "geodesic ghor algebras", a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t-structure, and an introduction to methods of constructive category theory.
• Altri titoli varianti: Representations of algebras, geometry and physics
• Titolo autorizzato: Representations of Algebras, Geometry and Physics
• ISBN: 9781470464257; 147046425X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910962803703321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary Mathematics