The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling...

Coxeter group is the affine Weyl group of An (the affine symmetric group). For n = 2, this can be pictured as a subgroup of the symmetry group of the standard...

groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics, the symmetric...

The orthogonal group O(2), another infinite generalization of the finite dihedral groups The affine symmetric group, a family of groups including the infinite...

important class of algebraic groups is given by the affine algebraic groups, those whose underlying algebraic variety is an affine variety; they are exactly...

irreducible hermitian symmetric space of the form G/(U(1) · K), then both H and C*· H are non-symmetric irreducible affine holonomy groups, where V the tangent...

indeterminates. Therefore, the symmetric algebra over V can be viewed as a "coordinate free" polynomial ring over V. The symmetric algebra S(V) can be built...

In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector...

the vector in Zn. The affine group acts transitively on the points of an affine space, and the subgroup V of the affine group (that is, a vector space)...

cardinality of the affine group of an affine space with p elements. It follows that, if p is a prime number greater than 3, the symmetric group and the alternating...