Richard Brauer

Richard Brauer (1901–1977) was a German-born mathematician whose work helped establish modern representation theory and the theory of algebras, especially through the development of modular representation theory.

Representation theory: The study of algebraic structures through their actions on vector spaces. Brauer’s research made representations a central tool for studying finite groups.
Brauer character: A character associated with a representation over a field of positive characteristic, defined on elements of order prime to that characteristic. These characters provided modular counterparts to ordinary group characters.
University of Königsberg: A historic university in Königsberg, Prussia, where Brauer studied mathematics. Brauer’s mathematical education began at this university.
Richard Brauer Prize: An award of the American Mathematical Society recognizing outstanding work in algebra. The prize bears Brauer’s name in recognition of his influence on algebra.
Group representation: A homomorphism from a group to the invertible linear transformations of a vector space. Group representations were the main objects Brauer analyzed and classified.
Brauer induction theorem: A theorem expressing characters of finite groups as integer combinations induced from elementary subgroups. It reduces global character questions to representations of more manageable subgroups.
Issai Schur: A Russian-born German mathematician known for foundational work in representation theory and algebra. Schur supervised Brauer’s doctoral work and helped shape his early mathematical direction.
Finite group: A group with finitely many elements. Brauer’s methods became foundational tools for understanding representations of finite groups.
Group algebra: An algebra built from formal linear combinations of elements of a group. Brauer connected the representation theory of groups to the structure of their algebras.
Brauer–Nesbitt theorem: A theorem relating semisimple representations through their character values. It supplies a key bridge between character calculations and module structure.

Linked from 9 pages