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257521010
Representation Theory: A First Course: 129 (Graduate Texts in Mathematics, 129)
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257521010
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This text is designed for beginners to learn from and not as a reference.
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What Stands Out
Comprehensive Coverage
Offers a thorough introduction to representation theory, making complex concepts accessible for graduate students and advanced undergraduates in mathematics and physics.
Clear Explanations
Utilizes clear and concise language, supplemented with numerous examples, to effectively convey intricate topics, ensuring better understanding and retention.
Practical Applications
Demonstrates the application of representation theory in various fields, providing readers with insights into its relevance and practicality in real-world problems.
Product Details
- The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.
| Publisher | Springer |
| Publication date | 22 Oct. 1991 |
| Edition | 1st Corrected ed. 2004. Corr. 3rd printing 1999 |
| Language | English |
| Print length | 566 pages |
| ISBN-10 | 0387974954 |
| ISBN-13 | 978-0387974958 |
| Item weight | 850 g |
| Dimensions | 15.49 x 3.25 x 23.5 cm |
| Part of series | Graduate Texts in Mathematics |
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Algebra Editorial Review
Representation Theory: A First Course: 129 (Graduate Texts In Mathematics, 129) offers an extensive exploration of representation theory, ideal for graduate students in mathematics. Published by Springer, this comprehensive text spans 566 pages and is presented in a well-structured format that encourages deep understanding. The book, with its first corrected edition published in 2004, incorporates various examples and exercises that reinforce key concepts in representation theory. Readers have praised its clarity and pedagogical approach, making it suitable for both self-study and classroom use. The dimensions and weight ensure a sturdy yet manageable textbook experience.
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Pros
- In-depth exploration of representation theory concepts
- Clear explanations and pedagogical approach
- Extensive examples and exercises included
- Well-structured for self-study and teaching
- Sturdy hardcover format for lasting use
Cons
- Some complex topics may require prior knowledge
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Features & Benefits
- Targeted at beginners in representation theory.
- Focuses on finite-dimensional representations of Lie groups and algebras.
- Unique approach compared to other texts in the field.
- Emphasizes the importance of group actions in 20th century mathematics.
- Covers material in a clear and accessible manner.
- Ideal for mathematicians beyond just specialists.
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