Group of Lie type information

specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive...

In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...

200. This is the only simple group that is a derivative of a group of Lie type that is not strictly a group of Lie type in any series due to exceptional...

simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be...

exceptions are the sporadic groups. The Tits group is sometimes regarded as a sporadic group because it is not strictly a group of Lie type, in which case there...

the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic. The proof consists of tens of thousands of pages...

chapter of linear algebra. A group of Lie type is a group closely related to the group G(k) of rational points of a reductive linear algebraic group G with...

all families of non-abelian finite simple groups may be considered to be of Lie type. One of 16 families of groups of Lie type The Tits group is generally...

(In this case, the Lie bracket measures the failure of commutativity for the Lie group.) Conversely, to any finite-dimensional Lie algebra over the real...

classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26...

group of Lie type over a field of characteristic 2. In the classification of finite simple groups, there is a major division between group of characteristic...

mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree (1960, 1961) from an exceptional automorphism of a Dynkin diagram...

mathematician Sophus Lie (/liː/ LEE) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that...

quasithin group is a finite simple group that resembles a group of Lie type of rank at most 2 over a field of characteristic 2. The classification of quasithin...

Classical Groups. The classical groups form the deepest and most useful part of the subject of linear Lie groups. Most types of classical groups find application...

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...

G(22n+1), form an infinite family of groups of Lie type found by Suzuki (1960), that are simple for n ≥ 1. These simple groups are the only finite non-abelian...

Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups...

representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the...

M} . Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded...

include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in...

In mathematics, the indefinite orthogonal group, O(p, q) is the Lie group of all linear transformations of an n-dimensional real vector space that leave...

algebraic K-theory. Steinberg group (Lie theory) is a 'twisted' group of Lie type, in particular one of the groups of type 3D4 or 2E6. This disambiguation...