Finite Reflection Groups [electronic resource] /
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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Language: | eng |
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New York, NY : Springer New York : Imprint: Springer,
1985
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Subjects: | Mathematics., Group theory., Group Theory and Generalizations., |
Online Access: | http://dx.doi.org/10.1007/978-1-4757-1869-0 |
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KOHA-OAI-TEST:2211162018-07-30T23:59:09ZFinite Reflection Groups [electronic resource] / Grove, L. C. author. Benson, C. T. author. SpringerLink (Online service) textNew York, NY : Springer New York : Imprint: Springer,1985.engChapter 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.1 Preliminaries -- 2 Finite Groups in Two and Three Dimensions -- 3 Fundamental Regions -- 4 Coxeter Groups -- 5 Classification of Coxeter Groups -- 6 Generators and Relations for Coxeter Groups -- 7 Invariants -- Postlude -- Crystallographic Point Groups -- References.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.Mathematics.Group Theory and Generalizations.Springer eBookshttp://dx.doi.org/10.1007/978-1-4757-1869-0URN:ISBN:9781475718690 |
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Mathematics. Group theory. Mathematics. Group Theory and Generalizations. Mathematics. Group theory. Mathematics. Group Theory and Generalizations. |
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Mathematics. Group theory. Mathematics. Group Theory and Generalizations. Mathematics. Group theory. Mathematics. Group Theory and Generalizations. Grove, L. C. author. Benson, C. T. author. SpringerLink (Online service) Finite Reflection Groups [electronic resource] / |
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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. |
format |
Texto |
topic_facet |
Mathematics. Group theory. Mathematics. Group Theory and Generalizations. |
author |
Grove, L. C. author. Benson, C. T. author. SpringerLink (Online service) |
author_facet |
Grove, L. C. author. Benson, C. T. author. SpringerLink (Online service) |
author_sort |
Grove, L. C. author. |
title |
Finite Reflection Groups [electronic resource] / |
title_short |
Finite Reflection Groups [electronic resource] / |
title_full |
Finite Reflection Groups [electronic resource] / |
title_fullStr |
Finite Reflection Groups [electronic resource] / |
title_full_unstemmed |
Finite Reflection Groups [electronic resource] / |
title_sort |
finite reflection groups [electronic resource] / |
publisher |
New York, NY : Springer New York : Imprint: Springer, |
publishDate |
1985 |
url |
http://dx.doi.org/10.1007/978-1-4757-1869-0 |
work_keys_str_mv |
AT grovelcauthor finitereflectiongroupselectronicresource AT bensonctauthor finitereflectiongroupselectronicresource AT springerlinkonlineservice finitereflectiongroupselectronicresource |
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1756270256209264640 |