Lie group
group that is also a smooth manifold with group operations that are smooth
simple Lie group
type of Lie group
projective unitary group
quotient of special unitary group by its center
projective linear group
construction in group theory
Carnot group
simply connected nilpotent Lie group equipped with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra
classical group
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.)
compact Lie group
Lie group which is also a compact manifold
solvable Lie group
algebraic structure
special linear group
group of linear transformations with determinant 1
general linear group
n x n invertible matrices over a ring
affine group
Group of all affine transformations of an affine space
Euclidean group
isometry group of Euclidean space
Heisenberg group
Lie group of 3×3 upper triangular matrices under matrix multiplication
projective orthogonal group
twofold quotient of the orthogonal group: PO(n) = O(n)/{±1}