Related papers: On unipotent algebraic G-groups and 1-cohomology

The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to…

Let R be a semi-local regular domain containing an infinite perfect field k, and let K be the field of fractions of R. Let G be a reductive semi-simple simply connected R-group scheme such that each of its R-indecomposable factors is…

Let $\Sigma$ be a finite type surface, and $G$ a complex algebraic simple Lie group with Lie algebra $\mathfrak{g}$. The quantum moduli algebra of $(\Sigma,G)$ is a quantization of the ring of functions of $X_G(\Sigma)$, the variety of…

Let G be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of G, in particular in the cases where G is ramified. We establish a local Langlands correspondence for this class of…

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed…

This paper gives a new explicit construction of the $\mathbb{Q}$-algebraic hull for virtually solvable groups $\Gamma$ of finite abelian ranks, taking into account the spectrum $S$ of the group $\Gamma$. As an application, we make a…

Let $G$ be a finitely generated group with polynomial growth, and let $\om$ be a weight, i.e. a sub-multiplicative function on $G$ with positive values. We study when the weighted group algebra $\ell^1(G,\om)$ is isomorphic to an operator…

In 2011, Guralnick and Tiep proved that if $G$ was a Chevalley group with Borel subgroup $B$ and $V$ an irreducible $G$-module in cross characteristic with $V^B = 0$, then the the dimension of $H^1(G,V)$ is determined by the structure of…

Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…

Let $G$ be a finite group. To every smooth $G$-action on a compact, connected and oriented Riemann surface we can associate its data of singular orbits. The set of such data becomes an Abelian group $B_G$ under the $G$-equivariant connected…

Let $G$ be a finite abelian group acting faithfully on ${\mathbb C}{\mathbb P}^1$ via holomorphic automorphisms. In \cite{DF2} the $G$--equivariant algebraic vector bundles on $G$--invariant affine open subsets of ${\mathbb C}{\mathbb P}^1$…

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we extend a well-known result about the Picard group of a semisimple group to reductive…

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

Let G be the set of k-points of a connected semisimple algebraic group of k-rank one over a nonarchimedean local field k. We describe all finitely generated torsion-free discrete subgroups of G\times G acting properly discontinuously and…

We study the structure of Lie groups admitting left invariant abelian complex structures in terms of commutative associative algebras. If, in addition, the Lie group is equipped with a left invariant Hermitian structure, it turns out that…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

The modular group algebra of an elementary abelian p-group is isomorphic to the restricted enveloping algebra of commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures…

We describe the structure of Sylow {\ell}-subgroups of a finite reduc-tive group G(Fq) when q $\not\equiv$ 0 (mod {\ell}) that we find governed by a complex reflection group attached to G and {\ell}, which depends on {\ell} only through the…