Topic
Reductive group
About: Reductive group is a research topic. Over the lifetime, 2645 publications have been published within this topic receiving 65306 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 1991
TL;DR: Conventions and notation background material from algebraic geometry general notions associated with algebraic groups homogeneous spaces solvable groups Borel subgroups reductive groups rationality questions are discussed in this paper.
Abstract: Conventions and notation background material from algebraic geometry general notions associated with algebraic groups homogeneous spaces solvable groups Borel subgroups reductive groups rationality questions.
3,072 citations
Book•
1 Jan 1975
TL;DR: A survey of rationality properties of semisimple groups can be found in this paper, where a survey of rational properties of algebraic groups is also presented, as well as a classification of reductive groups representations.
Abstract: Algebraic geometry affine algebraic groups lie algebras homogeneous spaces chracteristic 0 theory semisimple and unipoten elements solvable groups Borel subgroups centralizers of Tori structure of reductive groups representations and classification of semisimple groups survey of rationality properties.
2,437 citations
1 Jan 1973
2,371 citations
TL;DR: In this article, the irreducible representations of semisimple algebraic groups of characteristic p 0 were studied, in particular the rational representations, and all of the representations of corresponding finite simple groups.
Abstract: Our purpose here is to study the irreducible representations of semisimple algebraic groups of characteristic p 0, in particular the rational representations, and to determine all of the representations of corresponding finite simple groups. (Each algebraic group is assumed to be defined over a universal field which is algebraically closed and of infinite degree of transcendence over the prime field, and all of its representations are assumed to take place on vector spaces over this field.)
1,547 citations
Book•
1 Jan 1981
TL;DR: A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of polynomial equations in the matrix coordinates as mentioned in this paper.
Abstract: A linear algebraic group over an algebraically closed field k is a subgroup of a group GL n (k) of invertible n × n-matrices with entries in k, whose elements are precisely the solutions of a set of polynomial equations in the matrix coordinates. The present article contains a review of the theory of linear algebraic groups.
1,507 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 10 |
| 2024 | 11 |
| 2023 | 58 |
| 2022 | 109 |
| 2021 | 125 |
| 2020 | 114 |