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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.
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.
Vera Serganova is Professor of Mathematics at University of California, Berkeley.
Contains an application of quivers to the Harish-Chandra modules for SL(2)
Focuses on representations of finite groups
Includes expositions of the theory of representations of quivers along with substatial material on continuous groups
Introduces more advanced topics, such as representations of quantum groups and representations over non-Archimedean local fields, in an elementary way that is accessible to students
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xiii
223 S. |
| ISBN-13: | 9783319982694 |
| ISBN-10: | 3319982699 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-98269-4 |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Serganova, Vera
Gruson, Caroline |
| Auflage: | 1st edition 2018 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 14 mm |
| Von/Mit: | Vera Serganova (u. a.) |
| Erscheinungsdatum: | 26.10.2018 |
| Gewicht: | 0,371 kg |
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