Lie groups

group that is also a smooth manifold with group operations that are smooth

matrices important in quantum mechanics and the study of spin

vector space with an alternating binary operation satisfying the Jacobi identity.

group of isometries of Minkowski spacetime

subgroup of a real vector space

group that is a topological space with continuous group action

n x n invertible matrices over a ring

mathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed point

group of unitary matrices with determinant of 1

left-invariant (or right-invariant) measure on locally compact topological group

fractional linear transformation on the complex projective line

Lie group of Lorentz transformations

matrix operation generalizing exponentiation of scalar numbers

invariant symmetric bilinear form defined on Lie algebra; trace of composition of two adjoint representations

set of complex numbers whose absolute value is equal 1; Lie group of complex numbers of unit modulus; topologically a circle

group of unitary matrices

geometric arrangements of points, foundational to Lie theory

Lie group of 3×3 upper triangular matrices under matrix multiplication

group of matrices preserving a non-degenerate alternating quadratic form

group of rotations in 3 dimensions

248-dimensional exceptional simple Lie group

representation of invertible matrices as unitaries multiplying a Hermitian operator

group of linear transformations with determinant 1

topological space that is the space of cosets of a topological group

subgroup of a root system's isometry group

generalization of periodic functions to have group domains

formula in Lie theory

mathematical group which is the double cover of the special orthogonal group SO(n)

preprint

representation of a Lie group on its Lie algebra

mathematical problem posed by David Hilbert in 1900, concerning the characterization of Lie groups

study of Lie groups, Lie algebras and differential equations

linear algebraic group over a field such that, after base change to its algebraic closure, every smooth connected solvable normal subgroup is trivial

rotation composed with a reflection

In mathematics, the special linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: \mbox{SL}(2,\mathbf{R}) = \left\{ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \colon a,b,c,d \in \mathbf{R}\mbox{ and }ad-bc=1\right\}.

groups representable as matrix groups over a real division associative algebra (reals, complexes, or quaternions) that preserve a certain bilinear form (symmetric, skew-symmetric, Hermitian, skew-Hermitian, etc.)

isometry group of Euclidean space

construction in group theory

theorem about sufficient conditions for ensuring that that several elements in a group acting on a set freely generate a free subgroup of that group

on a Lie group G, a canonical 1-form valued in its own Lie algebra; the unique principal-bundle connection on the unique G-bundle over the one-point space

topological group with compact topology

symmetry-based invariance to continuous group action

i 78-dimensional exceptional simple Lie group

type of Lie group

Lie group homomorphism from the real numbers

Group of all affine transformations of an affine space

smooth group homomorphism from a Lie group to the general linear group of a vector space

maximal compact connected Abelian Lie subgroup

type of 2D conformal field theory

topological algebra associated to continuous groups

pseudo-Riemannian manifold whose symmetry group contains an inversion symmetry about every point

simple Lie group; the automorphism group of the octonions

map from Lie algebra to Lie group

discrete group of Möbius transformations

concept in geometry

concept in topology

limiting form of small transformation

orthogonal group of a space equipped with a metric of indefinite signature

formula of matrix exponentials

52-dimensional exceptional simple Lie group