UID:
almafu_9959234625702883
Format:
1 online resource (199 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88172-8
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1-107-36618-6
,
1-107-37091-4
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1-107-36127-3
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1-107-36947-9
,
1-299-40398-0
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1-107-36372-1
,
0-511-56577-1
Series Statement:
London Mathematical Society lecture note series ; 116
Content:
In this book the latest developments in representation theory are surveyed in a series of expository articles based on lectures given at the 1985 LMS Durham Symposium on representations of algebras. The emphasis is on the representation type of finite-dimensional algebras. Topics covered include almost split sequences, the theory of tubes, tilting functions, hammocks, and triangulated categories. There are also papers on the representation type of local rings of singularities, and on recent results in the modular representation theory of finite groups. All the articles are designed to be self contained and should be a useful aid to someone wishing to bring themselves up to date in the subject.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Title; copyright; Contents; Introduction; Representation theory of finite-dimensional algebras; LECTURE 1 : THE AUSLANDER-REITEN QUIVER; LECTURE 2 : SEPARATING SUBCATEGORIES: CONNECTING COMPONENTS AND SEPARATING TUBULAR FAMILIES; LECTURE 3 : REPETITIVE ALGEBRAS; References; A survey of existence theorems for almost split sequences; References; Representations of posets and tame matrix problems; 1. The theory of matrix problems can be considered in a natural; 2. Posets of finite type; 3. Tame schurian categories; Literature; Geometry of representations of quivers; INTRODUCTION
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1. QUIVERS AND REPRESENTATIONS2. THE REPRESENTATION SPACE OF A QLIVER; 3. THE FUNDAMENTAL SET; 4. INDECOMPOSABLES AND ROOT SYSTEMS; 5. PROOF OF THE FUNDAMENTAL LEMMA; REFEBENCES; Cohen-Macaulay modules on hypersurface singularities; 1. SIMPLE HYPERSURFACE SINGULARITIES; 1.1 Notation; 1.2 Families of Hypersurface Singularities; 1.3 The Classification of Simple Singularities; 2. HYPERSURFACE SINGULARITIES OF DIMENSION ONE AND TWO; 2.1 Maximal Cohen-Macaulay Modules; 2.2 Group Representations; 2.3 Vectorbundles on the Desingularisation; 2.4 Simple Plane Curve Singularities
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3. HYPERSURFACE SINGULARITIES OF FINITE COHEN-MACAULAY TYPE3.1 Matrix Factorisations; 3.2 Double branched Covers; 3.3 Constructing Families of MCM's; 4. Miscellaneous Remarks; REFERENCES; Almost split sequences and algebraic geometry; 1. Complete rational double points; 2. Protective curves; 3. Finite Cohen-Macaulay type; References; Representation rings of finite groups; Preface; FIRST LECTURE : Nilpotent elements in representation rings; 1. TENSOR PRODUCTS; 2. ALMOST SPLIT SEQUENCES; 3. NILPOTENT ELEMENTS IN A(G); 4. COHOMOLOGICAL CONSTRUCTION OF NILPOTENT ELEMENTS
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SECOND LECTURE : VARIETIES FOR MODULES : A SAMPLE CALCULATION1. Definitions and basic properties; 2. Cohomology of the dihedral two-groups; 3. MODULES FOR THE DIHEDRAL TWO-GROUPS; 4. THE VARIETIES FOR THE INDECOMPOSABLE kD2n -MODULES; REFERENCES
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English
Additional Edition:
ISBN 0-521-31288-4
Language:
English
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