Finite Reflection Groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1985
|
| Edition: | Second Edition |
| Series: | Graduate Texts in Mathematics, A Selection
99 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude |
| Physical Description: | 1 Online-Ressource (X, 136 p) |
| ISBN: | 9781475718690 9781441930729 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-1869-0 |
Staff View
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| 500 | |a Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude | ||
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Record in the Search Index
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475718690 9781441930729 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (X, 136 p) |
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| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics, A Selection |
| spelling | Grove, L. C. Verfasser aut Finite Reflection Groups by L. C. Grove, C. T. Benson Second Edition New York, NY Springer New York 1985 1 Online-Ressource (X, 136 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics, A Selection 99 0072-5285 Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude Mathematics Group theory Group Theory and Generalizations Mathematik Benson, C. T. Sonstige oth https://doi.org/10.1007/978-1-4757-1869-0 Verlag Volltext |
| spellingShingle | Grove, L. C. Finite Reflection Groups Mathematics Group theory Group Theory and Generalizations Mathematik |
| title | Finite Reflection Groups |
| title_auth | Finite Reflection Groups |
| title_exact_search | Finite Reflection Groups |
| title_full | Finite Reflection Groups by L. C. Grove, C. T. Benson |
| title_fullStr | Finite Reflection Groups by L. C. Grove, C. T. Benson |
| title_full_unstemmed | Finite Reflection Groups by L. C. Grove, C. T. Benson |
| title_short | Finite Reflection Groups |
| title_sort | finite reflection groups |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik |
| url | https://doi.org/10.1007/978-1-4757-1869-0 |
| work_keys_str_mv | AT grovelc finitereflectiongroups AT bensonct finitereflectiongroups |