العربية
中国
Français
Deutsch
Ελληνική
हिन्दी
Italiano
日本語
Português
Русский
EspañolRICHARD BRAUER
(Redirected from Brauer)
'Richard Dagobert Brauer' (February 10, 1901 - April 17, 1977) was a leading German and Jewish American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
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.
The Brauer-Fowler theorem, published in 1956, later provided significant
impetus towards the classification of finite simple groups, for it
implied that there could only be finitely many finite simple groups for
which the centralizer of an involution ( element of order ''2'') had
a specified structure.
Brauer applied modular representation theory to obtain subtle
information about group characters, particularly via his
three main theorems. These methods
were particularly useful in the classification of finite simple
groups with low rank Sylow ''2''-subgroups. The Brauer-Suzuki theorem
showed that no finite simple group could have a generalized quaternion
Sylow ''2''-subgroup, and the Alperin-Brauer-Gorenstein theorem
classified finite groups with wreathed or quasidihedral Sylow
''2''-subgroups. The methods developed by Brauer were also instrumental
in contributions by others to the classification program: for example,
the Gorenstein-Walter theorem, classifying finite groups with
a dihedral Sylow ''2''-subgroup, and Glauberman's
Z
★ -theorem. The theory of a block with a cyclic defect group, first worked out by Brauer in the case when the principal
block has defect group of order ''p'', and later worked out in full
generality by E.C. Dade, also had several applications to group theory,
for example to finite groups of matrices over the complex numbers in
small dimension. The Brauer tree is a combinatorial object associated
to a block with cyclic defect group which encodes much information about the structure of the block.
★ Brauer algebra, also called central simple algebra
★ Brauer group, the equivalence classes of brauer algebras over the same field ''F'' equipped with a group operation
★ Brauer-Nesbitt theorem
★ Brauer-Manin obstruction
★ Brauer-Siegel theorem
★ Brauer's theorem
★ Brauer's theorem on induced characters
★ Brauer characters
★ Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer, Curtis, C.W., , , American Mathematical Society and London Mathematical Society, 1999, ISBN 0-8218-9002-6
★
★
'Richard Dagobert Brauer' (February 10, 1901 - April 17, 1977) was a leading German and Jewish American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
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.
The Brauer-Fowler theorem, published in 1956, later provided significant
impetus towards the classification of finite simple groups, for it
implied that there could only be finitely many finite simple groups for
which the centralizer of an involution ( element of order ''2'') had
a specified structure.
Brauer applied modular representation theory to obtain subtle
information about group characters, particularly via his
three main theorems. These methods
were particularly useful in the classification of finite simple
groups with low rank Sylow ''2''-subgroups. The Brauer-Suzuki theorem
showed that no finite simple group could have a generalized quaternion
Sylow ''2''-subgroup, and the Alperin-Brauer-Gorenstein theorem
classified finite groups with wreathed or quasidihedral Sylow
''2''-subgroups. The methods developed by Brauer were also instrumental
in contributions by others to the classification program: for example,
the Gorenstein-Walter theorem, classifying finite groups with
a dihedral Sylow ''2''-subgroup, and Glauberman's
Z
★ -theorem. The theory of a block with a cyclic defect group, first worked out by Brauer in the case when the principal
block has defect group of order ''p'', and later worked out in full
generality by E.C. Dade, also had several applications to group theory,
for example to finite groups of matrices over the complex numbers in
small dimension. The Brauer tree is a combinatorial object associated
to a block with cyclic defect group which encodes much information about the structure of the block.
| Contents |
| See also |
| References |
| External links |
See also
★ Brauer algebra, also called central simple algebra
★ Brauer group, the equivalence classes of brauer algebras over the same field ''F'' equipped with a group operation
★ Brauer-Nesbitt theorem
★ Brauer-Manin obstruction
★ Brauer-Siegel theorem
★ Brauer's theorem
★ Brauer's theorem on induced characters
★ Brauer characters
References
★ Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer, Curtis, C.W., , , American Mathematical Society and London Mathematical Society, 1999, ISBN 0-8218-9002-6
External links
★
★
This article provided by Wikipedia. To edit the contents of this article, click here for original source.
psst.. try this: add to faves
