Representations of algebras : tame and wild behavior / José Antonio de la Peña.
Series Algebra and applications ; v. 30Editor: Cham : Springer [2020]Descripción: xiv, 233 p. : il. ; 24 cmISBN: 9783031122873 Tema(s): Representations of groupsOtra clasificación: 16Gxx (05Exx 18Axx 18Exx)1 Introduction and First Examples [1] -- 1.1 General Algebraic Problem [1] -- 1.2 Some Tcrminologx on Quadratic Forms [4] -- 1.3 Geometrical and Linear Aspects of Unit Forms [8] -- 1.4 Fundamental Examples [14] -- 1.5 Some Categorical Notions [20] -- 1.6 A Quick Overview on Algebraic Geometry [28] -- References [30] -- 2 A Categorical Approach [33] -- 2.1 Morphisms Between Indecomposable Modules [33] -- 2.2 Harada-Sai Sequences [36] -- 2.3 The Remak-Krull-Schmidt-Azumay a Decomposition [39] -- 2.4 First Elements of Auslander-Reiten Theory [42] -- 2.5 The Category of Additive Functors [45] -- 2.6 First Brauer-Thral I Conjecture [51] -- References [52] -- 3 Constructive Methods [55] -- 3.1 The Lattice of Ideals [55] -- 3.2 Other Brauer-Thrall Conjectures [62] -- 3.3 The Post-Projective Components of a Triangular Algebra [64] -- 3.4 A Generalization of Jacobi's Criterion [69] -- 3.5 The Tits Quadratic Form 71 References [74] -- 4 Spectral Methods in Representation Theory [75] -- 4.1 Hereditary Algebras and the Coxeter Transformation [76] -- 4.2 Coxeter Spectrum in the Study of Indecomposable Modules [81] -- 4.3 The Canonical Representation of a Group of Symmetries [86] -- 4.4 The Automorphism Group of a Graph [92] -- 4.5 Canonical Algebras [95] -- 4.6 Self-Injective Algebras [99] -- 4.7 Further Spectral Properties [103] -- References [110] -- 5 Group Actions on Algebras and Module Categories [113] -- 5.1 The Group of Automorphisms of an Algebra [115] -- 5.2 Constructions of Algebras Associated to Groups of Automorphisms (Coverings and Smash Products) [118] -- 5.3 Coverings and the Representation Type of an Algebra [122] -- 5.4 Balanced Functors [131] -- 5.5 Galois Coverings of Algebras [136] -- 5.6 Cycle-Finite Algebras [140] -- References [146] -- 6 Reflections and Weyl Groups [149] -- 6.1 Vinberg’s Characterization of Dynkin Diagrams [149] -- 6.2 M-Matrices and Positivity [155] -- 6.3 Coxeter Matrices and Weyl Group [158] -- 6.4 Very Sharp Reflections [162] -- 6.5 On the Decomposition of the Coxeter Polynomial -- of an Algebra of Cyclotomic Type [167] -- References [169] -- 7 Simply Connected Algebras [171] -- 7.1 The Fundamental Group of a Triangular Algebra [171] -- 7.2 A Separation Property [177] -- 7.3 Strongly Simply Connected Algebras [178] -- 7.4 Tame Quasi-Tilted Algebras [182] -- 7.5 Weakly Separating Families of Coils [188] -- References [193] -- 8 Degenerations of Algebras [195] -- 8.1 Deformation Theory of Algebras: A Geometric Approach [195] -- 8.2 Degenerations of Algebras: A Homological Interpretation [199] -- 8.3 Thme and Wild Algebras: Definitions and Degeneration Property [204] -- 8.4 The Tits Quadratic Form and the Degeneration of Algebras [208] -- References [217] -- 9 Further Comments [219] -- 9.1 More on Dichotomy Problems [219] -- 9.2 Some Historical Notes [224] -- References [227] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 16 P419 (Browse shelf) | Available | A-9428 |
Includes bibliographical references and index.
1 Introduction and First Examples [1] --
1.1 General Algebraic Problem [1] --
1.2 Some Tcrminologx on Quadratic Forms [4] --
1.3 Geometrical and Linear Aspects of Unit Forms [8] --
1.4 Fundamental Examples [14] --
1.5 Some Categorical Notions [20] --
1.6 A Quick Overview on Algebraic Geometry [28] --
References [30] --
2 A Categorical Approach [33] --
2.1 Morphisms Between Indecomposable Modules [33] --
2.2 Harada-Sai Sequences [36] --
2.3 The Remak-Krull-Schmidt-Azumay a Decomposition [39] --
2.4 First Elements of Auslander-Reiten Theory [42] --
2.5 The Category of Additive Functors [45] --
2.6 First Brauer-Thral I Conjecture [51] --
References [52] --
3 Constructive Methods [55] --
3.1 The Lattice of Ideals [55] --
3.2 Other Brauer-Thrall Conjectures [62] --
3.3 The Post-Projective Components of a Triangular Algebra [64] --
3.4 A Generalization of Jacobi's Criterion [69] --
3.5 The Tits Quadratic Form 71 References [74] --
4 Spectral Methods in Representation Theory [75] --
4.1 Hereditary Algebras and the Coxeter Transformation [76] --
4.2 Coxeter Spectrum in the Study of Indecomposable Modules [81] --
4.3 The Canonical Representation of a Group of Symmetries [86] --
4.4 The Automorphism Group of a Graph [92] --
4.5 Canonical Algebras [95] --
4.6 Self-Injective Algebras [99] --
4.7 Further Spectral Properties [103] --
References [110] --
5 Group Actions on Algebras and Module Categories [113] --
5.1 The Group of Automorphisms of an Algebra [115] --
5.2 Constructions of Algebras Associated to Groups of Automorphisms (Coverings and Smash Products) [118] --
5.3 Coverings and the Representation Type of an Algebra [122] --
5.4 Balanced Functors [131] --
5.5 Galois Coverings of Algebras [136] --
5.6 Cycle-Finite Algebras [140] --
References [146] --
6 Reflections and Weyl Groups [149] --
6.1 Vinberg’s Characterization of Dynkin Diagrams [149] --
6.2 M-Matrices and Positivity [155] --
6.3 Coxeter Matrices and Weyl Group [158] --
6.4 Very Sharp Reflections [162] --
6.5 On the Decomposition of the Coxeter Polynomial --
of an Algebra of Cyclotomic Type [167] --
References [169] --
7 Simply Connected Algebras [171] --
7.1 The Fundamental Group of a Triangular Algebra [171] --
7.2 A Separation Property [177] --
7.3 Strongly Simply Connected Algebras [178] --
7.4 Tame Quasi-Tilted Algebras [182] --
7.5 Weakly Separating Families of Coils [188] --
References [193] --
8 Degenerations of Algebras [195] --
8.1 Deformation Theory of Algebras: A Geometric Approach [195] --
8.2 Degenerations of Algebras: A Homological Interpretation [199] --
8.3 Thme and Wild Algebras: Definitions and Degeneration Property [204] --
8.4 The Tits Quadratic Form and the Degeneration of Algebras [208] --
References [217] --
9 Further Comments [219] --
9.1 More on Dichotomy Problems [219] --
9.2 Some Historical Notes [224] --
References [227] --
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