Related papers: Relatively projective profinie groups
We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups…
We prove that affine Coxeter groups are profinitely rigid.
In this article we describe the general and special projectivity groups for all irreducible residues of all thick, irreducible, spherical buildings of type $ \mathsf{B_{n}}$, $ \mathsf{C_{n}}$ and $\mathsf{F_4}$, and rank at least 3. This…
The set of all closed subgroups of a profinite carries a natural profinite topology. This space of subgroups can be classified up to homeomorphism in many cases, and tight bounds placed on its complexity as expressed by its scattered…
We describe the classification of ranked definably quasi-Frobenius groups of odd type : dihedral configurations are isomorphic to PGL(2, K) for K an algebraically closed field of characteristic other than two; Frobenius groups are spilt and…
We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].
In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.
We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.
In the paper we describe the derivations of two $\mathbb{N}$-graded infinity-dimensional Lie algebras $\mathbf{n}_1$ and $\mathbf{n}_1$ what are positive parts of affine Kats-Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$, respectively. Then we…
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using…
We give two definitions of relative symplectic Steinberg group and show that they coincide.
We give a characterization of groups with twisted p-periodic cohomology in terms of group actions on mod p homology spheres. An equivalent algebraic characterization of such groups is also presented.
We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of…
Let $\mathcal{C}$ be a smooth, projective and geometrically integral curve defined over a finite field $\mathbb{F}$. Let $A$ be the ring of function of $\mathcal{C}$ that are regular outside a closed point $P$ and let $k=\mathrm{Quot}(A)$.…
We give a complete diffeomorphism classification of 1-connected manifolds (of dimension different from 4) whose integral homology is H(M)=Z+Z+Z.
We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.
We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
In this paper we investigate the third homology of the projective special linear group ${\rm PSL}_2(A)$. As a result of our investigation we prove a projective refined Bloch-Wigner exact sequence over certain class of rings. The projective…
For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.