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1. |
Record Nr. |
UNISA996466867403316 |
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Autore |
Erdmann Karin <1948-> |
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Titolo |
Blocks of tame representation type and related algebras / / Karin Erdmann |
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Pubbl/distr/stampa |
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Berlin, Germany ; ; New York, New York : , : Springer, , [1990] |
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©1990 |
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ISBN |
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Edizione |
[1st ed. 1990.] |
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Descrizione fisica |
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1 online resource (XVI, 312 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1428 |
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Disciplina |
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Soggetti |
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Modular representations of groups |
Tame algebras |
Group rings |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (pages [307]-312). |
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Nota di contenuto |
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Algebras, quivers, representation type, Auslander-Reiten theory, coverings -- Special biserial algebras and the local semidihedral algebra -- Tame symmetric local algebras -- More on modules, quivers, Auslander-Reiten sequences -- Stable Auslander-Reiten components for tame blocks -- Algebras of dihedral type -- Algebras of guaternion type -- Algebras of semidihedral type -- Centres, blocks, decomposition numbers -- Some applications. |
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Sommario/riassunto |
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This monograph studies algebras that are associated to blocks of tame representation type. Over the past few years, a range of new results have been obtained and a comprehensive account of these is provided here to- gether with some new proofs of known results. Some general theory of algebras is also presented, as a means of understanding the subject. The book is addressed to researchers and graduate students interested in the links between representations of finite-dimensional algebras and modular group representation theory. The basic properties of modules and finite-dimensional algebras are assumed known. |
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2. |
Record Nr. |
UNISA996485661003316 |
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Autore |
Heuts Gijs |
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Titolo |
Simplicial and dendroidal homotopy theory / / Gijs Heuts, Ieke Moerdijk |
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Pubbl/distr/stampa |
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Cham, : Springer Nature, 2022 |
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Cham : , : Springer International Publishing AG, , 2022 |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (xx, 612 pages) : illustrations |
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Collana |
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Ergebnisse der Mathematik und ihrer Grenzgebiete ; v.75 |
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Altri autori (Persone) |
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Soggetti |
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Homotopy theory |
Teoria de l'homotopia |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Part I The Elementary Theory of Simplicial and Dendroidal Sets 1 Operads 2 Simplicial Sets 3 Dendroidal Sets 4 Tensor Products of Dendroidal Sets 5 Kan Conditions for Simplicial Sets 6 Kan Conditions for Dendroidal Sets Part II The Homotopy Theory of Simplicial and Dendroidal Sets 7 Model Categories 8 Model Structures on the Category of Simplicial Sets 9 Three Model Structures on the Category of Dendroidal Sets Part III The Homotopy Theory of Simplicial and Dendroidal Spaces 10 Reedy Categories and Diagrams of Spaces 11 Mapping Spaces and Bousfield Localizations 12 Dendroidal Spaces and ∞-Operads 13 Left Fibrations and the Covariant Model Structure 14 Simplicial Operads and ∞-Operads Epilogue References Index |
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Sommario/riassunto |
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This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully |
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developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization. |
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