A Journey Through Representation Theory
From Finite Groups to Quivers via Algebras
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Beschreibung
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.
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.
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
Autor*in
Caroline Gruson
Themen in »A Journey Through Representation Theory«
Artinian rings Peter-Weyl theorem continuous groups representation theory of finite groups representations of algebras representations of quivers invariant forms Orthogonality relations Harish-Chandra modules application quivers textbook representation theory graduate mathematics text Schur-Weyl duality self-adjoint Hopf algebras SL(2) modules