Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H . The homogeneous space G/H admits an affine embedding if and only if G/H is a quasi-affine algebraic variety. We start with some basic properties of affine embeddings and consider the cases, where the theory is well-de...

The famous Burnside–Schur theorem states that every primitive finite permutation group containing a regular cyclic subgroup is either 2-transitive or isomorphic to a subgroup of a 1-dimensional affine group of prime degree. It is known that this theorem can be expressed as a statement on Schur rings over a finite cyclic group. Generalizing the latter, Schur rings are introduced over a finite co...

Various topics on affine rings are considered, such as the relationship between Gelfand-Kirillov dimension and Krull dimension, and when a "locally affine" algebra is affine. The dimension result is applied to study prime ideals in fixed rings of finite groups, and in identity components of group-graded rings. 0. Introduction. We study affine rings (i.e., rings finitely generated as algebras ov...

We show that a tower of torsors under affine group schemes can be dominated by a torsor. Moreover, if the base is the spectrum of a field and the structure group schemes are finite, the tower can be dominated by a finite torsor. As an application, we show that if X is a torsor under a finite group scheme G over a scheme S which has a fundamental group scheme, then X has a fundamental group sche...

We prove triviality of the centre arbitrary Hecke algebras irreducible non-finite non-affine type. This result is obtained as a consequence following structure for conjugacy classes underlying Coxeter groups. If W any infinite group and w∈W nontrivial element that assumed not to be translation in case affine, then there an sequence conjugates w by generators whose length non-decreasing tends in...

Finite affine groups are given by groups of translations and di- lations on finite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.

The main goal of the paper is to show that the fully commutative elements in the affine Coxeter group e Cn form a union of two-sided cells. Then we completely answer the question of when the fully commutative elements of W form or do not form a union of two-sided cells in the case where W is either a finite or an affine Coxeter group. Let W be a Coxeter group with S the distinguished generator ...

for some n , acting primitively on the set of vertices. This forms a part of the programme for the classification of all finite primitive distance transitive graphs begun in [76]; for in [76] this classification is reduced to the determination of all such graphs whose automorphism group G is either almost simple (that is, T o f f S Aut T for some nonabelian simple group T ) or affine (that is, ...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called emph{affine subgroups.}~the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_...

It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (respectively, any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there exists a pseudo-holomorphic curve (a Hurwitz curve) in CP whose fundamental group of the complement is not Hopfian and, respectively, this group is not...