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Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
This modern translation of Sophus Lie's and Friedrich Engel's
"Theorie der Transformationsgruppen 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 volume is 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.
Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
This modern translation of Sophus Lie's and Friedrich Engel's
“Theorie der Transformationsgruppen 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 volume is 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.
In diesem Monat feiern wir den 150. Geburtstag von SOPHUS LIE,
einem der groessten Mathematiker des vorigen Jahrhunderts. Es ist
daher sehr zu begrussen, dass der Teubner Verlag, einer langen
Traditionslinie bei der Veroeffentlichung von LIES Werken folgend,
in seine Reihe "TEUBNER-ARCHIV zur Mathematik" Arbeiten von SOPHUS
LIE und seinen Zeitgenossen EDuARD STUDY und FRIEDRICH ENGEL
aufgenommen hat. Ausgewahlt wurden Beitrage zur Theorie der
Differentialinvarianten. Zum einen ist dies ein Gebiet, auf dem
alle drei tatig gewesen sind und das als Ausgangspunkt grosser
Liescher Ideen zur Anwendung gruppentheoretischer Methoden in der
Analysis betrachtet werden kann, obwohl es nur einen Ausschnitt aus
LIES Schaffen darstellt. Zum anderen vermitteln die hier
vorgestellten Arbeiten durch ihren kritischen Stil und durch den
Streit um unterschied liche mathematische Auffassungen interessante
Einblicke in das mathematische Geschehen jener Zeit. Neben der
Wurdigung dieser drei namhaften Mathematiker stellt der vorliegende
Band den Ursprung der Lieschen Theorie, ihre weitere Entwicklung
und spatere Auspragung dar. Wir danken dem Teubner-Verlag und
insbesondere Herrn J. WEISS fur das freundliche Entgegenkommen und
die gute Zusammenarbeit. Greifswald und Leipzig, Dezember 1992
GUENTER CZICHOWSKI BERND FRITZSCHE SOPHUS LIE OElgemalde von ERIK
THEODOR WERENSKIOLD aus dem Jahre 1902; im Besitz der Universitat
Oslo (Katalognummer 818) Inhalt S. Lie: UEber Gruppen von
Transformationen, 1874. (Gesammelte Abhandlungen, Bd. 5 (1924),1-8)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 S. Lie: UEber Differentialinvarianten, 1884. (Gesammelte
Abhandlungen, Bd. 6 (1927), 95-l38) . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 16 . . . . . . . S. Lie: UEber die Gruppe
der Bewegungen und ihre Differentialinvarianten, 1893. (Gesammelte
Abhandlungen, Bd. 6 (1927), 376-383) . . . . . . . . . . . . . . .
Das Halten einer Antrittsvorlesung gehArte zu den bewAhrten
Traditionen der deutschen UniversitAten. Diese Reden spiegelten in
der Regel die Ansichten des Neuberufenen zu allgemeinen Fragen
seiner Wissenschaft wider, nicht selten auch programmatische
Vorstellungen A1/4ber das zukA1/4nftige Wirken. Sie waren so
gehalten, daA sie einem breiten Publikum verstAndlich blieben. Die
vorliegende Sammlung Leipziger mathematischer Antrittsvorlesungen
der Jahre 1869 bis 1922 enthAlt fotomechanische Nachdrucke der
entsprechenden Reden von Carl Neumann, Felix Klein, Sophus Lie,
Friedrich Engel, Felix Hausdorff, Heinrich Liebmann, Wilhelm
Blaschke und Leon Lichtenstein. Das Buch wird ergAnzt durch kurze
Biographien dieser Gelehrten sowie durch einige aufschluAreiche,
teilweise noch unverAffentlichte Archivalien.
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