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Theory of transformation groups: general properties of continuous transformation groups ; a contemporary approach and translation 1

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Beteilige Person:	Lie, Sophus 1842-1899 (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2015
Links:	https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 https://doi.org/10.1007/978-3-662-46211-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027945818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027945818&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	1 Online-Ressource
ISBN:	9783662462119
DOI:	10.1007/978-3-662-46211-9

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Datensatz im Suchindex

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adam_text	THEORY OF TRANSFORMATION GROUPS I / LIE, SOPHUS : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS PART I MODERN PRESENTATION 1 THREE PRINCIPLES OF THOUGHT GOVERNING THE THEORY OF LIE 2 LOCAL TRANSFORMATION EQUATIONS AND ESSENTIAL PARAMETERS 3 FUNDAMENTAL DIFFERENTIAL EQUATIONS FOR FINITE CONTINUOUS TRANSFORMATION GROUPS 4 ONE-TERM GROUPS AND ORDINARY DIFFERENTIAL.- PART II ENGLISH TRANSLATION 5 COMPLETE SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS 7 DETERMINATION OF ALL SYSTEMS OF EQUATIONS WHICH ADMIT GIVEN INFINITESIMAL TRANSFORMATIONS 8 COMPLETE SYSTEMS WHICH ADMIT ALL TRANSFORMATIONS OF A ONE-TERM GROUP 9 CHARACTERISTIC RELATIONSHIPS BETWEEN THE INFINITESIMAL TRANSFORMATIONS OF A GROUP 10 SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS THE GENERAL SOLUTION OF WHICH DEPENDS ONLY UPON A FINITE NUMBER OF ARBITRARY CONSTANTS 11 THE DEFINING EQUATIONS FOR THE INFINITESIMAL TRANSFORMATIONS OF A GROUP 12 DETERMINATION OF ALL SUBGROUPS OF AN R-TERM GROUP 13 TRANSITIVITY, INVARIANTS 14 DETERMINATION OF ALL SYSTEMS OF EQUATIONS WHICH ADMIT A GIVEN R-TERM GROUP 15 INVARIANT FAMILIES OF INFINITESIMAL TRANSFORMATIONS 16 THE ADJOINT GROUP 17 COMPOSITION AND ISOMORPHISM 18 FINITE GROUPS, THE TRANSFORMATIONS OF WHICH FORM DISCRETE CONTINUOUS FAMILIES 19 THEORY OF THE SIMILARITY [AEHNLICHKEIT] OF R-TERM GROUPS 20 GROUPS, THE TRANSFORMATIONS OF WHICH ARE INTERCHANGEABLE WITH ALL TRANSFORMATIONS OF A GIVEN GROUP 21 THE GROUP OF PARAMETERS 22 THE DETERMINATION OF ALL R-TERM GROUPS 23 INVARIANT FAMILIES OF MANIFOLDS.- 24 SYSTATIC AND ASYSTATIC TRANSFORMATION GROUPS 25 DIFFERENTIAL INVARIANTS 26 THE GENERAL PROJECTIVE GROUP 27 LINEAR HOMOGENEOUS GROUPS 28 APPROACH [ANSATZ] TOWARDS THE DETERMINATION OF ALL FINITE CONTINUOUS GROUPS OF THE N-TIMES EXTENDED SPACE 29 CHARACTERISTIC PROPERTIES OF THE GROUPS WHICH ARE EQUIVALENT TO CERTAIN PROJECTIVE GROUPS GLOSSARY OF SIGNIFICANTLY USED WORDS INDEX./P DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. THEORY OF TRANSFORMATION GROUPS I / LIE, SOPHUS : 2015 ABSTRACT / INHALTSTEXT THIS MODERN TRANSLATION OF SOPHUS LIE S AND FRIEDRICH ENGEL S “THEORIE DER TRANSFORMATIONSGRUPPEN BAND I” WILL ALLOW READERS TO DISCOVER THE STRIKING CONCEPTUAL CLARITY AND REMARKABLY SYSTEMATIC ORGANIZATIONAL THOUGHT OF THE ORIGINAL GERMAN TEXT. VOLUME I PRESENTS A COMPREHENSIVE INTRODUCTION TO THE THEORY AND IS MAINLY DIRECTED TOWARDS THE GENERALIZATION OF IDEAS DRAWN FROM THE STUDY OF EXAMPLES. THE MAJOR PART OF THE PRESENT VOLUME OFFERS AN EXTREMELY CLEAR TRANSLATION OF THE LUCID ORIGINAL. THE FIRST FOUR CHAPTERS PROVIDE NOT ONLY A TRANSLATION, BUT ALSO A CONTEMPORARY APPROACH, WHICH WILL HELP PRESENT DAY READERS TO FAMILIARIZE THEMSELVES WITH THE CONCEPTS AT THE HEART OF THE SUBJECT. THE EDITOR S MAIN OBJECTIVE WAS TO ENCOURAGE A RENEWED INTEREST IN THE DETAILED CLASSIFICATION OF LIE ALGEBRAS IN DIMENSIONS 1, 2 AND 3, AND TO OFFER ACCESS TO SOPHUS LIE S MONUMENTAL GALOIS THEORY OF CONTINUOUS TRANSFORMATION GROUPS, ESTABLISHED AT THE END OF THE 19TH CENTURY. LIE GROUPS ARE WIDESPREAD IN MATHEMATICS, PLAYING A ROLE IN REPRESENTATION THEORY, ALGEBRAIC GEOMETRY, GALOIS THEORY, THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS, AND ALSO IN PHYSICS, FOR EXAMPLE IN GENERAL RELATIVITY. THIS VOLUMEIS OF INTEREST TO RESEARCHERS IN LIE THEORY AND EXTERIOR DIFFERENTIAL SYSTEMS AND ALSO TO HISTORIANS OF MATHEMATICS. THE PREREQUISITES ARE A BASIC KNOWLEDGE OF DIFFERENTIAL CALCULUS, ORDINARY DIFFERENTIAL EQUATIONS AND DIFFERENTIAL GEOMETRY DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spellingShingle	Lie, Sophus 1842-1899 Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation
title	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation
title_alt	Theorie der Transformationsgruppen
title_auth	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation
title_exact_search	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation
title_full	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation 1 Sophus Lie. Ed. and transl.: Joël Merker
title_fullStr	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation 1 Sophus Lie. Ed. and transl.: Joël Merker
title_full_unstemmed	Theory of transformation groups general properties of continuous transformation groups ; a contemporary approach and translation 1 Sophus Lie. Ed. and transl.: Joël Merker
title_short	Theory of transformation groups
title_sort	theory of transformation groups general properties of continuous transformation groups a contemporary approach and translation
title_sub	general properties of continuous transformation groups ; a contemporary approach and translation
url	https://doi.org/10.1007/978-3-662-46211-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027945818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027945818&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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