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Richard Brauer
Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
Alfred Brauer was Richard's brother and seven years older. They were born to a Jewish family. Both were interested in science and mathematics, but Alfred was injured in combat in World War I. As a boy, Richard dreamt of becoming an inventor, and in February 1919 enrolled in Technische Hochschule Berlin-Charlottenburg. He soon transferred to University of Berlin. Except for the summer of 1920 when he studied at University of Freiburg, he studied in Berlin, being awarded his PhD on 16 March 1926. Issai Schur conducted a seminar and posed a problem in 1921 that Alfred and Richard worked on together, and published a result. The problem also was solved by Heinz Hopf at the same time. Richard wrote his thesis under Schur, providing an algebraic approach to irreducible, continuous, finite-dimensional representations of real orthogonal (rotation) groups.
Ilse Karger also studied mathematics at the University of Berlin; she and Brauer were married 17 September 1925. Their sons George Ulrich (born 1927) and Fred Gunther (born 1932) also became mathematicians. Brauer began his teaching career in Königsberg (now Kaliningrad) working as Konrad Knopp’s assistant. Brauer expounded central division algebras over a perfect field while in Königsberg; the isomorphism classes of such algebras form the elements of the Brauer group he introduced.
When the Nazi Party took over in 1933, the Emergency Committee in Aid of Displaced Foreign Scholars took action to help Brauer and other Jewish scientists. Brauer was offered an assistant professorship at University of Kentucky. Brauer accepted the offer, and by the end of 1933 he was in Lexington, Kentucky, teaching in English. Ilse followed the next year with George and Fred; brother Alfred made it to the United States in 1939, but their sister Alice was killed in the Holocaust.
Hermann Weyl invited Brauer to assist him at Princeton's Institute for Advanced Study in 1934. Brauer and Nathan Jacobson edited Weyl's lectures Structure and Representation of Continuous Groups. Through the influence of Emmy Noether, Brauer was invited to University of Toronto to take up a faculty position. With his graduate student Cecil J. Nesbitt he developed modular representation theory, published in 1937. Robert Steinberg, Stephen Arthur Jennings, and Ralph Stanton were also Brauer’s students in Toronto. Brauer also conducted international research with Tadasi Nakayama on representations of algebras. In 1941 University of Wisconsin hosted visiting professor Brauer. The following year he visited the Institute for Advanced Study and Bloomington, Indiana where Emil Artin was teaching.
In 1948, Brauer moved to Ann Arbor, Michigan where he and Robert M. Thrall contributed to the program in modern algebra at University of Michigan.
In 1952, Brauer joined the faculty of Harvard University and retired in 1971. His students included Donald John Lewis, Donald Passman, and I. Martin Isaacs. Brauer was elected to the American Academy of Arts and Sciences in 1954, the United States National Academy of Sciences in 1955, and the American Philosophical Society in 1974. The Brauers frequently traveled to see their friends such as Reinhold Baer, Werner Wolfgang Rogosinski, and Carl Ludwig Siegel.
Several theorems bear his name, including Brauer's induction theorem, which has applications in number theory as well as finite group theory, and its corollary Brauer's characterization of characters, which is central to the theory of group characters.
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Richard Brauer
Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
Alfred Brauer was Richard's brother and seven years older. They were born to a Jewish family. Both were interested in science and mathematics, but Alfred was injured in combat in World War I. As a boy, Richard dreamt of becoming an inventor, and in February 1919 enrolled in Technische Hochschule Berlin-Charlottenburg. He soon transferred to University of Berlin. Except for the summer of 1920 when he studied at University of Freiburg, he studied in Berlin, being awarded his PhD on 16 March 1926. Issai Schur conducted a seminar and posed a problem in 1921 that Alfred and Richard worked on together, and published a result. The problem also was solved by Heinz Hopf at the same time. Richard wrote his thesis under Schur, providing an algebraic approach to irreducible, continuous, finite-dimensional representations of real orthogonal (rotation) groups.
Ilse Karger also studied mathematics at the University of Berlin; she and Brauer were married 17 September 1925. Their sons George Ulrich (born 1927) and Fred Gunther (born 1932) also became mathematicians. Brauer began his teaching career in Königsberg (now Kaliningrad) working as Konrad Knopp’s assistant. Brauer expounded central division algebras over a perfect field while in Königsberg; the isomorphism classes of such algebras form the elements of the Brauer group he introduced.
When the Nazi Party took over in 1933, the Emergency Committee in Aid of Displaced Foreign Scholars took action to help Brauer and other Jewish scientists. Brauer was offered an assistant professorship at University of Kentucky. Brauer accepted the offer, and by the end of 1933 he was in Lexington, Kentucky, teaching in English. Ilse followed the next year with George and Fred; brother Alfred made it to the United States in 1939, but their sister Alice was killed in the Holocaust.
Hermann Weyl invited Brauer to assist him at Princeton's Institute for Advanced Study in 1934. Brauer and Nathan Jacobson edited Weyl's lectures Structure and Representation of Continuous Groups. Through the influence of Emmy Noether, Brauer was invited to University of Toronto to take up a faculty position. With his graduate student Cecil J. Nesbitt he developed modular representation theory, published in 1937. Robert Steinberg, Stephen Arthur Jennings, and Ralph Stanton were also Brauer’s students in Toronto. Brauer also conducted international research with Tadasi Nakayama on representations of algebras. In 1941 University of Wisconsin hosted visiting professor Brauer. The following year he visited the Institute for Advanced Study and Bloomington, Indiana where Emil Artin was teaching.
In 1948, Brauer moved to Ann Arbor, Michigan where he and Robert M. Thrall contributed to the program in modern algebra at University of Michigan.
In 1952, Brauer joined the faculty of Harvard University and retired in 1971. His students included Donald John Lewis, Donald Passman, and I. Martin Isaacs. Brauer was elected to the American Academy of Arts and Sciences in 1954, the United States National Academy of Sciences in 1955, and the American Philosophical Society in 1974. The Brauers frequently traveled to see their friends such as Reinhold Baer, Werner Wolfgang Rogosinski, and Carl Ludwig Siegel.
Several theorems bear his name, including Brauer's induction theorem, which has applications in number theory as well as finite group theory, and its corollary Brauer's characterization of characters, which is central to the theory of group characters.
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