An introduction to the representation theory of groups / Emmanuel Kowalski.
Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as cl...
Saved in:
| Main Author: | |
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| Language: | English |
| Published: |
Providence, Rhode Island :
American Mathematical Society,
[2014]
|
| Series: | Graduate studies in mathematics ;
v. 155. |
| Subjects: | |
| Physical Description: | vi, 432 pages : illustrations ; 27 cm. |
| Format: | Book |
MARC
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| 100 | 1 | |a Kowalski, Emmanuel, |d 1969- |e author. |0 http://id.loc.gov/authorities/names/n2004002624 | |
| 245 | 1 | 3 | |a An introduction to the representation theory of groups / |c Emmanuel Kowalski. |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c [2014] | |
| 264 | 4 | |c ©2014 | |
| 300 | |a vi, 432 pages : |b illustrations ; |c 27 cm. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics ; |v volume 155 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Chapter 1: Introduction and motivation -- Presentation -- Four motivating statements -- Prerequisites and notation -- Chapter 2: The language of representation theory -- Basic language -- Formalism: changing the space -- Formalism: changing the group - Formalism: changing the field -- Matrix representations -- Examples -- Some general results -- Some Clifford theory -- Conclusion -- Chapter 3: Variants -- Representations of algebras -- Representations of Lie algebras -- Topological groups -- Unitary representations -- Chapter 4: Linear representations of finite groups -- Maschke's Theorem -- Applications of Maschke's Theorem -- Decomposition of representations -- Harmonic analysis on finite groups -- Finite abelian groups -- The character table -- Applications -- Further topics -- Chapter 5: Abstract representation theory of compact groups -- An example: the circle group -- The Haar measure and the regular representation of a locally compact group -- The analogue of the group algebra -- The Peter-Weyl Theorem -- Characters and matrix coefficients for compact gropus -- Some first examples -- Chapter 6: Applications of representations of compact groups -- Compact Lie groups are matrix groups -- The Frobenius-Schur indicator -- The Larsen alternative -- The hydrogen atom -- Chapter 7: Other groups: a few examples -- Algebraic groups - Locally compact groups: general remarks -- Locally compact abelian groups -- A non-abelian example: SL2(R) -- Appendix A. Some useful facts. A.1. Algebraic integers -- A.2. The spectral theorem -- A.3. The Stone-Weierstrass Theorem. | |
| 520 | |a Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples. --Provided by publisher. | ||
| 650 | 0 | |a Lie groups. |0 http://id.loc.gov/authorities/subjects/sh85076786. |0 http://id.loc.gov/authorities/subjects/sh85076786 | |
| 650 | 0 | |a Representations of groups. |0 http://id.loc.gov/authorities/subjects/sh85112944. |0 http://id.loc.gov/authorities/subjects/sh85112944 | |
| 650 | 0 | |a Group algebras. |0 http://id.loc.gov/authorities/subjects/sh85057472. |0 http://id.loc.gov/authorities/subjects/sh85057472 | |
| 830 | 0 | |a Graduate studies in mathematics ; |v v. 155. |0 http://id.loc.gov/authorities/names/n92111274. |0 http://id.loc.gov/authorities/names/n92111274 | |
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