A journey through representation theory from finite groups to quivers via algebras
This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory...
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| Weitere Verfasser: | , |
| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cham
Springer International Publishing
2018
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| Schriftenreihe: | Universitext
Mathematics |
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| Online Zugang: | Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings Introduction to Representation Theory of Finite Groups -- Modules with Applications to Finite Groups -- Representations of Compact Groups -- Results About Unitary Representations -- On Algebraic Methods -- Symmetric Groups, Schur-Weyl Duality and Positive Self-adjoint Hopf Algebras -- Introduction to representation theory of quivers -- Representations of Dynkin and affine quivers -- Applications of quivers -- Bibliography -- Index |
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| Beschreibung: | Literaturverzeichnis: Seite 219-220 |
| Beschreibung: | xiii, 223 Seiten Diagramme |
| ISBN: | 9783319982694 978-3-319-98269-4 |