A Journey Through Representation Theory
Springer International Publishing (Verlag)
978-3-319-98269-4 (ISBN)
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.
Caroline Gruson is Professor of Mathematics at Université de Lorraine. Vera Serganova is Professor of Mathematics at University of California, Berkeley.
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.
| Erscheinungsdatum | 28.10.2018 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | XIII, 223 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 373 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | application quivers • artinian rings • continuous groups • graduate mathematics text • Harish-Chandra modules • invariant forms • Orthogonality relations • Peter-Weyl Theorem • Representations of algebras • Representations of quivers • representation theory of finite groups • Schur-Weyl duality • self-adjoint Hopf algebras • SL(2) modules • textbook representation theory |
| ISBN-10 | 3-319-98269-9 / 3319982699 |
| ISBN-13 | 978-3-319-98269-4 / 9783319982694 |
| Zustand | Neuware |
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