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Claude Chevalley
Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group. Life His father, Abel Chevalley, was a French diplomat who, jointly with his wife Marguerite Chevalley née Sabatier, wrote ''The Concise Oxford French Dictionary''. Chevalley graduated from the École Normale Supérieure in 1929, where he studied under Émile Picard. He then spent time at the University of Hamburg, studying under Emil Artin and at the University of Marburg, studying under Helmut Hasse. In Germany, Chevalley discovered Japanese mathematics in the person of Shokichi Iyanaga. Chevalley was awarded a doctorate in 1933 from the University of Paris for a thesis on class field theory. When World War II broke out, Chevalley was at Princeton University. After reporting to the French Embass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Johannesburg
Johannesburg ( , , ; Zulu language, Zulu and Xhosa language, Xhosa: eGoli ) (colloquially known as Jozi, Joburg, Jo'burg or "The City of Gold") is the most populous city in South Africa. With 5,538,596 people in the City of Johannesburg alone and over 14.8 million in the urban agglomeration, it is classified as a Megacity#List of megacities, megacity and List of urban areas by population, one of the 100 largest urban areas in the world. Johannesburg is the provinces of South Africa, provincial capital of Gauteng, the wealthiest province in South Africa, and seat of the country's highest court, the Constitutional Court of South Africa, Constitutional Court. The city is located within the mineral-rich Witwatersrand hills, the epicentre of the international mineral and gold trade. The richest city in Africa by GDP and private wealth, Johannesburg functions as the economic capital of South Africa and is home to the continent's largest stock exchange, the Johannesburg Stock Exchang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chevalley Group
In mathematics, specifically in group theory, the phrase ''group of Lie type'' usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase ''group of Lie type'' does not have a widely accepted precise definition, but the important collection of finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups. The name "groups of Lie type" is due to the close relationship with the (infinite) Lie groups, since a compact Lie group may be viewed as the rational points of a reductive linear algebraic group over the field of real numbers. and are standard references for groups of Lie type. Classical groups An initial approach to this question was the definition and detailed study of the so-called ''classical groups'' over finite and other fields by . These groups were studied by L. E. Dickson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nouvelle Revue Française
''La Nouvelle Revue Française'' (; "The New French Review") is a literary magazine based in France. In France, it is often referred to as the ''NRF''. History and profile The magazine was founded in 1909 by a group of intellectuals including André Gide, Jacques Copeau, and Jean Schlumberger (writer), Jean Schlumberger. It was established 'in opposition to other, more established, cultural institutions, most notably the Académie Française and its associated networks'.:4 In 1911, Gaston Gallimard became editor of the ''Revue'', which led to the founding of the publishing house, Éditions Gallimard. During World War I its publication stopped. The magazine was relaunched in 1919. Established writers such as Paul Bourget and Anatole France contributed to the magazine from its early days. The magazine's influence grew until, during the interwar period, it became the leading literary journal, occupying a unique role in French culture. The first published works by André Malraux and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was one of the most influential mathematicians of the twentieth century. His influence is due both to his original contributions to a remarkably broad spectrum of mathematical theories, and to the mark he left on mathematical practice and style, through some of his own works as well as through the Bourbaki group, of which he was one of the principal founders. Life André Weil was born in Paris to agnostic Alsatian Jewish parents who fled the annexation of Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71. Simone Weil, who would later become a famous philosopher, was Weil's younger sister and only sibling. He studied in Paris, Rome and Göttingen and received his doctorate in 1928. While in Germany, Weil befriended Carl Ludwig Siegel. Starting in 1930, he spent two academic years at Aligarh Mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Shokichi Iyanaga
was a Japanese people, Japanese mathematician. Early life Iyanaga was born in Tokyo, Japan on April 2, 1906. He studied at the University of Tokyo from 1926 to 1929. He studied under Teiji Takagi. As an undergraduate, he published two papers in the ''Japanese Journal of Mathematics'' and the ''Proceedings of the Imperial Academy of Tokyo''. Both of his papers appeared in print in 1928. After completing his undergraduate degree in 1929, he stayed at Tokyo and worked under Takagi for his doctorate. He completed his Doctor of Philosophy, Ph.D. in mathematics 1931. Years in Europe In 1931, Iyanaga obtained a scholarship from the France, French government. He also went to Hamburg, Germany where he studied with Austrian mathematician Emil Artin. In 1932, he attended the International Congress of Mathematicians in Zurich. During his time in Europe, he met with top mathematicians such as Claude Chevalley, Henri Cartan, and others. Academic career Iyanaga returned to Tokyo in 1934 and w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Helmut Hasse
Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and diophantine geometry ( Hasse principle), and to local zeta functions. Life Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written Haße (12 April 1868 – 1 June 1940, son of Friedrich Ernst Hasse and his wife Anna Von Reinhard) and his wife Margarethe Louise Adolphine Quentin (born 5 July 1872 in Milwaukee, daughter of retail toy merchant Adolph Quentin (b. May 1832, probably Berlin, Kingdom of Prussia) and Margarethe Wehr (b. about 1840, Prussia), then raised in Kassel). After serving in the Imperial German Navy in World War I, he studied at the University of Göttingen, and then at the University of Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Mink ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Emil Artin
Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Along with Emmy Noether, he is considered the founder of modern abstract algebra. Early life and education Parents Emil Artin was born in Vienna to parents Emma Maria, née Laura (stage name Clarus), a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of mixed Austrians, Austrian and Armenian people, Armenian descent. His Armenian last name was Artinian which was shortened to Artin. Several documents, including Emil's birth certificate, list the father's occupation as "opera singer" though others list it as "art dealer." It see ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Émile Picard
Charles Émile Picard (; 24 July 1856 – 11 December 1941) was a French mathematician. He was elected the fifteenth member to occupy seat 1 of the Académie française in 1924. Life He was born in Paris on 24 July 1856 and educated there at the Lycée Henri-IV. He then studied mathematics at the École Normale Supérieure. Picard's mathematical papers, textbooks, and many popular writings exhibit an extraordinary range of interests, as well as an impressive mastery of the mathematics of his time. Picard's little theorem states that every nonconstant entire function takes every value in the complex plane, with perhaps one exception. Picard's great theorem states that an analytic function with an essential singularity takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity. He made important contributions in the theory of differential equations, including work on Picard–Vessiot theory, Painlevé transcendents and his introdu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Louis Auguste Sabatier
Louis Auguste Sabatier (; 22 October 1839 – 12 April 1901) was a French Protestant theologian. Biography He was born at Vallon-Pont-d'Arc, Ardèche and died in Strasbourg. He was educated at the Protestant theological faculty of Montauban as well as at the universities of Tübingen and Heidelberg. After holding the pastorate at Aubenas in Ardèche from 1864 to 1868, he was appointed professor of reformed dogmatics at the Protestant theological faculty of Strasbourg. His markedly French sympathies during the War of 1870 led to his expulsion from Strassburg in 1872. After five years' effort he succeeded in establishing a Protestant Faculty of Theology in Paris (today: Faculté de théologie protestante de Paris) along with Eugène Ménégoz, and became professor and then dean. In 1886, he became a teacher in the newly founded religious science department of the École des Hautes Etudes at the Sorbonne. His brother, Paul, was a noted theological historian. He is the father ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algebraic Groups
In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups, including orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties. An important class of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly the algebraic subgroups of the general linear group, and are therefore also called ''linear algebraic groups''. Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theorem states that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Finite Group Theory
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004. History During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be bui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
