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...

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...

called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic. (The Tits group is sometimes regarded as a sporadic group because...

971,200. This is the only simple group that is a derivative of a group of Lie type that is not a group of Lie type in any series from exceptional isomorphisms...

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...

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...

(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...

of non-abelian finite simple groups may be considered to be of Lie type. One of 16 families of groups of Lie type or their derivatives The Tits group...

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...

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation...

LIE, Lie, lie, dissemble, or fibbing in Wiktionary, the free dictionary. A lie is a type of deception, an untruth or not telling the truth. Lie, LIE or...

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...

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...

classification of finite simple groups of Lie type, 63 and 36 are both exponents that figure in the orders of three exceptional groups of Lie type. The orders of these...

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...

universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property...

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...

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...

defined as the unit group of the matrix ring M(n, R). The general linear group GL(n, R) over the field of real numbers is a real Lie group of dimension n2....

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...

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

mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support...

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...

pair is a structure on groups of Lie type that allows one to give uniform proofs of many results, instead of giving a large number of case-by-case proofs...

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...

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

suggests, many of the groups of Lie type over the field with 2 elements are groups of GF(2)-type. Also 16 of the 26 sporadic groups are of GF(2)-type, suggesting...

group T {\displaystyle \mathbb {T} } , which is the only finite simple group to classify as either a non-strict group of Lie type or sporadic group,...