سوفوس لي

سوفوس لي
Sophus Lie
Portrett av Sophus Lie.jpg
وُلِدَ(1842-12-17)17 ديسمبر 1842
نوردفيوردايد، النرويج
توفي18 فبراير 1899(1899-02-18) (aged 56)
كريستيانيا، النرويج
الجنسيةنرويجي
المدرسة الأمجامعة كريستيانيا
اللقبOne-parameter group
Differential invariant
Contact transformation
Infinitesimal transformation
W-curve
Carathéodory–Jacobi–Lie theorem
Lie algebra
Lie bracket
Lie group
Lie product formula
Lie sphere geometry
Lie theory
Lie transform
Lie's theorem
Lie's third theorem
Lie–Kolchin theorem
See full list
الجوائزوسام لوباتشيڤسكي (1897)
ForMemRS (1895)
السيرة العلمية
المجالاتالرياضيات
الهيئاتجامعة كريستيانيا
جامعة لايپزيگ
المشرف على الدكتوراهCarl Anton Bjerknes
Cato Maximilian Guldberg
طلاب الدكتوراهHans Blichfeldt
Lucjan Emil Böttcher
Gerhard Kowalewski
Kazimierz Żorawski
Élie Cartan
Elling Holst
Edgar Odell Lovett

ماريوس سوفوس لي ( Marius Sophus Lie ؛ /liː/ LEE؛ نرويجية: [liː] ؛ عاش 17 ديسمبر 1842 – 18 فبراير 1899) عالم رياضيات نرويجي، ذاعت شهرته بسبب عمله في نظرية المجموعات والهندسة التفاضلية. بعد أن درس في جامعة كريستيانيا بأوسلو، ذهب عام 1870 إلى باريس، حيث انكب على دراسة المجموعات التحويلية مع عالم الرياضيات الألماني فيلكس كلاين.

وعندما اندلعت الحرب الفرنسية البروسية في العام نفسه سافر لِي إلى إيطاليا وسويسرا. وفي عام 1872 عاد إلى أوسلو وأصبح أستاذًا للرياضيات في جامعة كريستيانا، حيث نشر عدة أعمال مهمة تتعلق بالمعادلات التفاضلية، وطَوَّر نظرية المجموعات التحويلية الرتيبة، وبالرغم من ذلك لم يلق إلا القليل من الاعتراف في النرويج. وفي عام 1886 ذهب لِي إلى ليبزج حيث تولى كرسي فيلكس كلاين، في الرياضيات. وفي لايبزج وجد أتباعاً، ولكنَّ صحته تدهورت بسرعة. وفي عام 1898 عاد إلى جامعة كريستيانيا حيث أنشأت الحكومة النرويجية كرسياً (قسماً دراسياً جامعياً) لنظرية المجموعات التحويلية.

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حياته وسيرته

Marius Sophus Lie was born on 17 December 1842 in the small town of Nordfjordeid. He was the youngest of six children born to Lutheran pastor Johann Herman Lie and his wife, who came from a well-known Trondheim family.[1]

He had his primary education in the south-eastern coast of Moss, before attending high school in Oslo (known then as Christiania). After graduating from high school, his ambition towards a military career was dashed when the army rejected him due to poor eyesight. He then enrolled at the University of Christiania.

Sophus Lie's first mathematical work, Repräsentation der Imaginären der Plangeometrie, was published in 1869 by the Academy of Sciences in Christiania and also by Crelle's Journal. That same year he received a scholarship and travelled to Berlin, where he stayed from September to February 1870. There, he met Felix Klein and they became close friends. When he left Berlin, Lie travelled to Paris, where he was joined by Klein two months later. There, they met Camille Jordan and Gaston Darboux. But on 19 July 1870 the Franco-Prussian War began and Klein (who was Prussian) had to leave France very quickly. Lie left for Fontainebleau where he was arrested, suspected of being a German spy, garnering him fame in Norway. He was released from prison after a month, thanks to the intervention of Darboux.[2]

Lie obtained his PhD at the University of Christiania (in present-day Oslo) in 1871 with a thesis entitled Over en Classe geometriske Transformationer (On a Class of Geometric Transformations).[3] It would be described by Darboux as "one of the most handsome discoveries of modern Geometry". The next year, the Norwegian Parliament established an extraordinary professorship for him. That same year, Lie visited Klein, who was then at Erlangen and working on the Erlangen program.

In 1872, Lie spent eight months together with Peter Ludwig Mejdell Sylow, editing and publishing the mathematical works of their countryman, Niels Henrik Abel.

At the end of 1872, Sophus Lie proposed to Anna Birch, then eighteen years old, and they were married in 1874. The couple had three children: Marie (b. 1877), Dagny (b. 1880) and Herman (b. 1884).

From 1876, he co-edited the journal Archiv for Mathematik og Naturvidenskab, together with the physician Jacob Worm-Müller, and the biologist Georg Ossian Sars.

In 1884, Friedrich Engel arrived at Christiania to help him, with the support of Klein and Adolph Mayer (who were both professors at Leipzig by then). Engel would help Lie to write his most important treatise, Theorie der Transformationsgruppen, published in Leipzig in three volumes from 1888 to 1893. Decades later, Engel would also be one of the two editors of Lie's collected works.

In 1886, Lie became a professor at Leipzig, replacing Klein, who had moved to Göttingen. In November 1889, Lie suffered a mental breakdown and had to be hospitalized until June 1890. Subsequently he returned to his post, but over the years his anaemia progressed to the point where he returned to his homeland. In 1898 he tendered his resignation in May, and left for home in September the same year. He died the following year in 1899 at the age of 56, due to pernicious anemia, a disease caused by impaired absorption of vitamin B12.

He was made Honorary Member of the London Mathematical Society in 1878, Corresponding Member of the French Academy of Sciences in 1892, Foreign Member of the Royal Society of London in 1895 and foreign associate of the National Academy of Sciences of the United States of America in 1895.

  • 1888 copy of "Theorie der Transformationsgruppen," volume I

    1888 copy of "Theorie der Transformationsgruppen," volume I

  • Title page to "Theorie der Transformationsgruppen"

    Title page to "Theorie der Transformationsgruppen"

  • Preface to "Theorie der Transformationsgruppen"

    Preface to "Theorie der Transformationsgruppen"


ذكراه

تمثال نصفي في مسقط رأسه نوردفيوردايد، 2019.

الأداة الرئيسية للي، وواحدة من أعظم انجازاته، كانت اكتشاف أن مجموعات التحويل المتصلة (الآن تسمى على اسمه مجموعات لي) يمكن فهمها بشكل أفضل بتحويلهم لصيغة "خطية"، ودراسة the corresponding generating vector fields (the so-called infinitesimal generators). The generators are subject to a linearized version of the group law, now called the commutator bracket, and have بنية ما يسمى اليوم جبر لي.[4][5]

استخدم هرمان ڤايل عمل لي في نظرية المجموعات في أوراقه البحثية من 1922 و 1923. واليوم، تلعب مجموعات لي دوراً في ميكانيكا الكم.[5] However, the subject of Lie groups as it is studied today is vastly different from what the research by Sophus Lie was about and "among the 19th century masters, Lie's work is in detail certainly the least known today".[6]

Sophus Lie was an eager proponent in the establishment of the Abel Prize. Inspired by the Nansen fund named after Fridtjof Nansen, and the lack of a prize for mathematics in the Nobel Prize. He gathered support for the establishment of an award for outstanding work in pure mathematics.[7]

Lie advised many doctoral students who went on to become successful mathematicians. Élie Cartan became widely regarded as one of the greatest mathematicians of the twentieth century. Kazimierz Żorawski's work was proved to be of importance to a variety of fields. Hans Frederick Blichfeldt made great contributions to various fields of mathematics.

كتبه

  • Lie, Sophus (1888) (in de), Theorie der Transformationsgruppen I, Leipzig: B. G. Teubner . Written with the help of Friedrich Engel. English translation available: Edited and translated from the German and with a foreword by Joël Merker, see ISBN 978-3-662-46210-2 and قالب:Arxiv
  • Lie, Sophus (1890) (in de), Theorie der Transformationsgruppen II, Leipzig: B. G. Teubner . Written with the help of Friedrich Engel.
  • Lie, Sophus (1891) (in de), Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen, Leipzig: B. G. Teubner . Written with the help of Georg Scheffers.[8]
  • Lie, Sophus (1893) (in de), Vorlesungen über continuierliche Gruppen, Leipzig: B. G. Teubner . Written with the help of Georg Scheffers.[9]
  • Lie, Sophus (1893) (in de), Theorie der Transformationsgruppen III, Leipzig: B. G. Teubner . Written with the help of Friedrich Engel.
  • Lie, Sophus (1896) (in de), Geometrie der Berührungstransformationen, Leipzig: B. G. Teubner . Written with the help of Georg Scheffers.[10]
  • Lie, Sophus, Engel, Friedrich, ed., Gesammelte Abhandlungen, Leipzig: Teubner, https://catalog.hathitrust.org/Record/005830809; 7 vols., 1922–1960 [11][12]

انظر أيضاً

الهامش

  1. ^ James, Ioan (2002). Remarkable Mathematicians. Cambridge University Press. p. 201. ISBN 978-0-521-52094-2.
  2. ^ Darboux, Gaston (1899). "Sophus Lie". Bull. Amer. Math. Soc. 5 (7): 367–370. doi:10.1090/s0002-9904-1899-00628-1.
  3. ^ Lie, Sophus (1871). Over en classe geometriske Transformationer (PhD). University of Christiania.
  4. ^ Helgason, Sigurdur (1994), "Sophus Lie, the Mathematician", Proceedings of the Sophus Lie Memorial Conference, Oslo, August, 1992, Oslo: Scandinavian University Press, pp. 3–21. 
  5. ^ أ ب Gale, Thomson. "Marius Sophus Lie Biography". World of Mathematics. Retrieved 23 January 2009.
  6. ^ Hermann, Robert, ed. (1975), Sophus Lie's 1880 transformation group paper, Lie groups: History, frontiers and applications, 1, Math Sci Press, p. iii, ISBN 0-915692-10-4 
  7. ^ "The History of the Abel Prize". www.abelprize.no. Retrieved 2021-02-04.
  8. ^ Lovett, E. O. (1898). "Review: Vorlesungen über Differentialgleichungen mit bekannten infinitesimalen Transformationen". Bull. Amer. Math. Soc. 4 (4): 155–167. doi:10.1090/s0002-9904-1898-00476-7.
  9. ^ Brooks, J. M. (1895). "Review: Vorlesungen über continuerliche Gruppen mit geometrischen und anderen Anwendungen". Bull. Amer. Math. Soc. 1 (10): 241–248. doi:10.1090/s0002-9904-1895-00283-9.
  10. ^ Lovett, E. O. (1897). "Review: Geometrie der Berührungstransformationen". Bull. Amer. Math. Soc. 3 (9): 321–350. doi:10.1090/s0002-9904-1897-00430-x.
  11. ^ Schilling, O. F. G. (1939). "Book Review: Sophus Lie's Gesammelte Abhandlungen. Geometrische Abhandlungen, Volumes I & II". Bulletin of the American Mathematical Society. 45 (7): 513–514. doi:10.1090/S0002-9904-1939-07032-8. ISSN 0002-9904.
  12. ^ Carmichael, R. D. (1930). "Book Review: vol. IV of Sophus Lie's Gesammelte Abhandlungen (Samlede Avhandlinger, Norwegian edition published by Aschehoug)". Bulletin of the American Mathematical Society. 36 (5): 337–338. doi:10.1090/S0002-9904-1930-04950-2. ISSN 0002-9904. (with links to 1923 review of Vol. III, 1925 review of Vol. V, & 1928 review of Vol. VI)

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