| Richard Brauer | |
 Richard Brauer
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| Born | February 10, 1901 |
|---|---|
| Died | April 17, 1977 |
| Nationality | United States, Germany |
| Fields | Scientist, Mathematician |
| Doctoral advisor | Issai Schur, Erhard Schmidt |
| Doctoral students | Cecil J. Nesbitt, Robert Steinberg |
| Known for | Brauer's theorem on induced characters |
Richard Dagobert Brauer (February 10, 1901 - April 17, 1977) was a leading German and American mathematician. Events 1355 - The St Scholastica's Day riot breaks out in Oxford, England, leaving 63 scholars and perhaps 30 locals dead Year 1901 ( MCMI) was a Common year starting on Tuesday (link will display calendar of the Gregorian calendar (or a Common year starting Events 69 - After the First Battle of Bedriacum, Vitellius becomes Roman Emperor. Also 1977 (album by Ash. Year 1977 ( MCMLXXVII) was a Common year starting on Saturday (link displays The United States of America —commonly referred to as the Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A scientist, in the broadest sense refers to any person that engages in a systematic activity to acquire Knowledge or an individual that engages in such practices A mathematician is a person whose primary area of study and research is the field of Mathematics. A doctorate is an Academic degree that indicates the highest level of academic achievement Issai Schur ( January 10, 1875 in Mogilyov &ndash January 10, 1941 in Tel Aviv) was a Mathematician who Erhard Schmidt ( January 13, 1876 – December 6, 1959) was a German Mathematician born in Dorpat (now Cecil James Nesbitt, PhD FSA MAAA (1912 – 2001 was born in Ontario, Canada. Robert Steinberg (born May 25[[ 922]] Soroki, Romania) is a mathematician at the University of California Los Angeles who invented the Brauer's theorem on induced characters, often known as Brauer's induction theorem and named after Richard Brauer, is a basic result in the branch of Mathematics known Events 1355 - The St Scholastica's Day riot breaks out in Oxford, England, leaving 63 scholars and perhaps 30 locals dead Year 1901 ( MCMI) was a Common year starting on Tuesday (link will display calendar of the Gregorian calendar (or a Common year starting Events 69 - After the First Battle of Bedriacum, Vitellius becomes Roman Emperor. Also 1977 (album by Ash. Year 1977 ( MCMLXXVII) was a Common year starting on Saturday (link displays Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. The United States of America —commonly referred to as the A mathematician is a person whose primary area of study and research is the field of Mathematics. He worked mainly in abstract algebra, but made important contributions to number theory. Abstract algebra is the subject area of Mathematics that studies Algebraic structures such as groups, rings, fields, modules Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes He was the founder of modular representation theory. Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group
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. Brauer's theorem on induced characters, often known as Brauer's induction theorem and named after Richard Brauer, is a basic result in the branch of Mathematics known Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes In Mathematics, a finite group is a group which has finitely many elements Brauer's theorem on induced characters, often known as Brauer's induction theorem and named after Richard Brauer, is a basic result in the branch of Mathematics known
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. The classification of the finite simple groups, also called the enormous theorem is believed to classify all finite simple groups. In Group theory, the centralizer and normalizer of a Subset S of a group G are Subgroups of G which
Brauer applied modular representation theory to obtain subtle information about group characters, particularly via his three main theorems. Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group Brauer's main theorems are three theorems in Representation theory of finite groups linking the blocks of a Finite group (in characteristic p These methods were particularly useful in the classification of finite simple groups with low rank Sylow 2-subgroups. In Mathematics, specifically Group theory, the Sylow theorems, named after Ludwig Sylow, form a partial converse to Lagrange's theorem, which 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. In Mathematics, the Brauer-Suzuki theorem states that if a finite group has a generalized quaternion Sylow 2-subgroup and no non-trivial Normal subgroups In Group theory, the quaternion group is a non-abelian group of order 8 In Mathematics, the Alperin--Brauer--Gorenstein theorem characterizes the finite Simple groups with quasidihedral or wreathed Sylow 2-subgroups. In Mathematics, the quasi-dihedral groups and semi-dihedral groups are non-abelian groups of order a power of 2 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. In Mathematics, a dihedral group is the group of symmetries of a Regular polygon, including both rotations and reflections George Glauberman (b 1941 New York City) is a Mathematician at the University of Chicago who works on Finite simple groups He proved the In mathematics George Glauberman 's Z* theorem states that if G is a Finite group and T is a Sylow 2-subgroup of G containing 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. Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group 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. Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group
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
- Curtis, C. In Ring theory and related areas of Mathematics a central simple algebra ( CSA) over a field K (also called a Brauer algebra In Mathematics, the Brauer group arose out of an attempt to classify Division algebras over a given field K. In Mathematics, given a set X and an Equivalence relation ~ on X, the equivalence class of an element a in X In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division Group theory is a mathematical discipline the part of Abstract algebra that studies the Algebraic structures known as groups. In mathematics the Brauer-Nesbitt theorem can refer to several different theorems proved by Richard Brauer and Cecil J In Mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of Algebraic There also is Brauer's theorem on induced characters. In Mathematics, Brauer's theorem, named for Richard Brauer, is a Brauer's theorem on induced characters, often known as Brauer's induction theorem and named after Richard Brauer, is a basic result in the branch of Mathematics known Modular representation theory is a branch of Mathematics, and is that part of Representation theory which studies Linear representations of Finite group W. (1999). Pioneers of representation theory: Frobenius, Burnside, Schur, and Brauer. American Mathematical Society and London Mathematical Society. ISBN 0-8218-9002-6.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Richard Brauer”, MacTutor History of Mathematics archive
- Richard Brauer at the Mathematics Genealogy Project
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