- Algebraic geometry
- >
- Algebraic varieties
- >
- Algebraic groups
- >
- Linear algebraic groups

- Algebraic structures
- >
- Lie groups
- >
- Algebraic groups
- >
- Linear algebraic groups

- Differential geometry
- >
- Lie groups
- >
- Algebraic groups
- >
- Linear algebraic groups

- Fields of abstract algebra
- >
- Group theory
- >
- Algebraic groups
- >
- Linear algebraic groups

- Manifolds
- >
- Lie groups
- >
- Algebraic groups
- >
- Linear algebraic groups

- Topological groups
- >
- Lie groups
- >
- Algebraic groups
- >
- Linear algebraic groups

Hyperspecial subgroup

In the theory of reductive groups over local fields, a hyperspecial subgroup of a reductive group G is a certain type of compact subgroup of G. In particular, let F be a nonarchimedean local field, O

Reductive group

In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representa

Special group (algebraic group theory)

In the theory of algebraic groups, a special group is a linear algebraic group G with the property that every principal G-bundle is locally trivial in the Zariski topology. Special groups include the

Special linear group

In mathematics, the special linear group SL(n, F) of degree n over a field F is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inv

Mirabolic group

In mathematics, a mirabolic subgroup of the general linear group GLn(k) is a subgroup consisting of automorphisms fixing a given non-zero vector in kn. Mirabolic subgroups were introduced by. The imag

Orthogonal group

In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension n that preserve a fixed point, where the group

Thin group (algebraic group theory)

In algebraic group theory, a thin group is a discrete Zariski-dense subgroup of G(R) that has infinite covolume, where G is a semisimple algebraic group over the reals. This is in contrast to a lattic

Cartan subgroup

In algebraic geometry, a Cartan subgroup of a connected linear algebraic group over an algebraically closed field is the centralizer of a maximal torus (which turns out to be connected). Cartan subgro

Linear algebraic group

In mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, de

Quasi-split group

In mathematics, a quasi-split group over a field is a reductive group with a Borel subgroup defined over the field. Simply connected quasi-split groups over a field correspond to actions of the absolu

Virasoro group

In abstract algebra, the Virasoro group or Bott–Virasoro group (often denoted by Vir) is an infinite-dimensional Lie group defined as the universal central extension of the group of diffeomorphisms of

Iwahori subgroup

In algebra, an Iwahori subgroup is a subgroup of a reductive algebraic group over a nonarchimedean local field that is analogous to a Borel subgroup of an algebraic group. A parahoric subgroup is a pr

General linear group

In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of tw

Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation In the study of indefinite orthogonal groups, the unit hyperbola forms the basis fo

Algebraic torus

In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by , , or , is a type of commutative affine algebraic group commonly found in projective algebraic geometry and t

Good filtration

In mathematical representation theory, a good filtration is a filtration of a representation of a reductive algebraic group G such that the subquotients are isomorphic to the spaces of sections F(λ) o

© 2023 Useful Links.