The Classical Groups : : Their Invariants and Representations (PMS-1) / / Hermann Weyl.
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever ap...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1946 |
Year of Publication: | 2016 |
Language: | English |
Series: | Princeton Landmarks in Mathematics and Physics ;
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Physical Description: | 1 online resource (336 p.) |
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Weyl, Hermann, author. aut http://id.loc.gov/vocabulary/relators/aut The Classical Groups : Their Invariants and Representations (PMS-1) / Hermann Weyl. Princeton, NJ : Princeton University Press, [2016] ©1946 1 online resource (336 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Landmarks in Mathematics and Physics ; 45 Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Table of Contents -- Chapter I. Introduction -- Chapter II. Vector Invariants -- Chapter III. Matric Algebras and Group Rings -- Chapter IV. The Symmetric Group and The Full Linear Group -- Chapter V. The Orthogonal Group -- Chapter VI. The Symplectic Group -- Chapter VII. Characters -- Chapter VIII. General Theory of Invariants -- Chapter IX. Matric Algebras Resumed -- Chapter X. Supplements -- Errata and Addenda -- Bibliography -- Supplementary Bibliography, mainly for the years 1940-1945 -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Continuous groups. Group theory. MATHEMATICS / Group Theory. bisacsh Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package 9783110501063 ZDB-23-PMS Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691057569 https://doi.org/10.1515/9781400883905?locatt=mode:legacy https://www.degruyter.com/isbn/9781400883905 Cover https://www.degruyter.com/document/cover/isbn/9781400883905/original |
language |
English |
format |
eBook |
author |
Weyl, Hermann, Weyl, Hermann, |
spellingShingle |
Weyl, Hermann, Weyl, Hermann, The Classical Groups : Their Invariants and Representations (PMS-1) / Princeton Landmarks in Mathematics and Physics ; Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Table of Contents -- Chapter I. Introduction -- Chapter II. Vector Invariants -- Chapter III. Matric Algebras and Group Rings -- Chapter IV. The Symmetric Group and The Full Linear Group -- Chapter V. The Orthogonal Group -- Chapter VI. The Symplectic Group -- Chapter VII. Characters -- Chapter VIII. General Theory of Invariants -- Chapter IX. Matric Algebras Resumed -- Chapter X. Supplements -- Errata and Addenda -- Bibliography -- Supplementary Bibliography, mainly for the years 1940-1945 -- Index |
author_facet |
Weyl, Hermann, Weyl, Hermann, |
author_variant |
h w hw h w hw |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Weyl, Hermann, |
title |
The Classical Groups : Their Invariants and Representations (PMS-1) / |
title_sub |
Their Invariants and Representations (PMS-1) / |
title_full |
The Classical Groups : Their Invariants and Representations (PMS-1) / Hermann Weyl. |
title_fullStr |
The Classical Groups : Their Invariants and Representations (PMS-1) / Hermann Weyl. |
title_full_unstemmed |
The Classical Groups : Their Invariants and Representations (PMS-1) / Hermann Weyl. |
title_auth |
The Classical Groups : Their Invariants and Representations (PMS-1) / |
title_alt |
Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Table of Contents -- Chapter I. Introduction -- Chapter II. Vector Invariants -- Chapter III. Matric Algebras and Group Rings -- Chapter IV. The Symmetric Group and The Full Linear Group -- Chapter V. The Orthogonal Group -- Chapter VI. The Symplectic Group -- Chapter VII. Characters -- Chapter VIII. General Theory of Invariants -- Chapter IX. Matric Algebras Resumed -- Chapter X. Supplements -- Errata and Addenda -- Bibliography -- Supplementary Bibliography, mainly for the years 1940-1945 -- Index |
title_new |
The Classical Groups : |
title_sort |
the classical groups : their invariants and representations (pms-1) / |
series |
Princeton Landmarks in Mathematics and Physics ; |
series2 |
Princeton Landmarks in Mathematics and Physics ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (336 p.) Issued also in print. |
contents |
Frontmatter -- Preface to the First Edition -- Preface to the Second Edition -- Table of Contents -- Chapter I. Introduction -- Chapter II. Vector Invariants -- Chapter III. Matric Algebras and Group Rings -- Chapter IV. The Symmetric Group and The Full Linear Group -- Chapter V. The Orthogonal Group -- Chapter VI. The Symplectic Group -- Chapter VII. Characters -- Chapter VIII. General Theory of Invariants -- Chapter IX. Matric Algebras Resumed -- Chapter X. Supplements -- Errata and Addenda -- Bibliography -- Supplementary Bibliography, mainly for the years 1940-1945 -- Index |
isbn |
9781400883905 9783110501063 9783110442496 9780691057569 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA385 |
callnumber-sort |
QA 3385 W495 41946 |
url |
https://doi.org/10.1515/9781400883905?locatt=mode:legacy https://www.degruyter.com/isbn/9781400883905 https://www.degruyter.com/document/cover/isbn/9781400883905/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.2 |
dewey-sort |
3512.2 |
dewey-raw |
512.2 |
dewey-search |
512.2 |
doi_str_mv |
10.1515/9781400883905?locatt=mode:legacy |
oclc_num |
962359241 |
work_keys_str_mv |
AT weylhermann theclassicalgroupstheirinvariantsandrepresentationspms1 AT weylhermann classicalgroupstheirinvariantsandrepresentationspms1 |
status_str |
n |
ids_txt_mv |
(DE-B1597)474317 (OCoLC)962359241 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
The Classical Groups : Their Invariants and Representations (PMS-1) / |
container_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package |
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1770176761920749568 |
fullrecord |
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