Mubarakzyanov's classification of low-dimensional real Lie algebras, published in Russian in 1963. It complements the article on Lie algebra in the area of abstract...

theory Table of Lie groups Classification of low-dimensional real Lie algebras Jacobson, Nathan (1971). Exceptional Lie Algebras. CRC Press. ISBN 0-8247-1326-5...

the first table for real Lie algebras. Classification of low-dimensional real Lie algebras Simple Lie group#Full classification Fulton, William; Harris...

over any field. Some Lie algebras of low dimension are described here. See the classification of low-dimensional real Lie algebras for further examples...

descriptions of redirect targets — a classification theorem for semisimple rings Classification of Clifford algebras Classification of low-dimensional real Lie algebras...

algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras. Given an integer n, the ring of real...

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

(finite-dimensional) division algebra with center K. For example, the central simple algebras over the reals are matrix algebras over either the reals or the...

orthogonal Lie algebra or special orthogonal Lie algebra. Over real numbers, these Lie algebras for different n are the compact real forms of two of the four...

conjugates of one another. In 7 Euclidean dimensions, the single spinor representation is 8-dimensional and real; no isomorphisms to a Lie algebra from another...

spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in M-theory it is 11-dimensional. In order to describe real physical phenomena...

neighborhood that is homeomorphic to an open subset of n {\displaystyle n} -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but...

extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry...

surface has real dimension 4, and it plays an important role in the study of smooth 4-manifolds. K3 surfaces have been applied to Kac–Moody algebras, mirror...

there are isomorphisms between low-dimensional spin groups and certain classical Lie groups, owing to low-dimensional isomorphisms between the root systems...

(or reductive) Lie group, can be done for all. Therefore, once the role of some low-dimensional Lie groups such as GL(2) in the theory of modular forms...

infinite-dimensional topological group.) Once this result is established, we see that H {\displaystyle H} is a one-dimensional Lie group central extension of G...

as commutative von Neumann algebras do. Together with Francis Murray, he produced a classification of von Neumann algebras. The direct integral construction...

isomorphic to the Lie algebra of SO(3), the rotation group. The Bianchi types refer to the classification of three-dimensional Lie algebras by the Italian...

matrices to accomplish tasks such as projecting a three-dimensional object onto a two-dimensional screen, corresponding to a theoretical camera observation;...

is a quotient of the tensor algebra of V enjoying a certain universal property and is typically infinite-dimensional. Nichols algebras appear naturally...

grouping of boundary components, and thus (1+1)-dimension TQFTs correspond to Frobenius algebras. Furthermore, we can consider simultaneously 4-dimensional, 3-dimensional...

GL(n, F), and is the projective linear group of (n − 1)-dimensional projective space, not n-dimensional projective space. A related group is the collineation...

of the Leech lattice, quotiented out by its center. There are only three finite-dimensional associative division algebras over the reals — the real numbers...

of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of...

Using linear algebra, a projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector...

of complex semisimple Lie groups and Lie algebras. McKay conjecture: in a group G {\displaystyle G} , the number of irreducible complex characters of...

manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2 n {\displaystyle 2n} , so its cohomology groups lie in degrees...

on separable C*-algebras. Klein geometry More specifically, it is a homogeneous space X together with a transitive action on X by a Lie group G, which...

form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero...