Related papers: Normality in group rings

Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and $U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let $\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that the…

In this paper, we discuss some well-known results and some open problems of the theory of $\sigma$-properties of a group related to the study of generalized $T$-groups.

We define a homomorphism from (a certain extension of) the fundamental group of the Hamiltonian automorphism group of a symplectic manifold to the group of invertibles in its quantum cohomology ring. The manifold must satify a technical…

We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$…

This paper is centered around the classical problem of extracting properties of a finite group $G$ from the ring isomorphism class of its integral group ring $\mathbb{Z} G$. This problem is considered via describing the unit group…

Let $U$ be a compact semisimple Lie group with complexification $G$ and associated Cartan involution $\Theta$. Let $\nu$ be an involutive complex Lie group automorphism of $G$ commuting with $\Theta$, and consider the associated semisimple…

Let k^[6] denote a polynomial ring in 6 variables over an algebraically closed field k of characteristic zero and consider the action of SL2(k) on k^[6] induced by the irreducible representation of SL2 of degree 5 (the binary quintic…

For any finite abelian group $G$ and commutative unitary ring $R$, by $R[G]$ we denote the group algebra over $R$. Let $T=(g_1,\ldots,g_{\ell})$ be a sequence over the group $G$. We say $T$ is algebraically zero-sum free over R if…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

In this article, we study twisted derivations of cyclic group rings. Let $R$ be a commutative ring with unity, $G$ be a finite cyclic group, and ($\sigma, \tau$) be a pair of $R$-algebra endomorphisms of the group algebra $RG$, which are…

Let V be a compact Kahler manifold. Let G' be a commutative subgroup of Aut(V) and U the set of elements of zero entropy of G'. Then U is a group and G' is isomorphic to the direct product of groups U and G where G is a subgroup of G' such…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

Given a surjective ring homomorphism, we study when the induced group homomorphism on unit groups is surjective. To this end, we introduce notions of generalized inverses and units, as well as a class of rings such that the set of closed…

$\textbf{Theorem 1.2.}$ For a ring $A$, the following conditions are equivalent. $\textbf{1)}$ $A$ is a right automorphism-invariant right non-singular ring. $\textbf{2)}$ $A$ is a right automorphism-invariant regular ring. $\textbf{3)}$…

For a group $G$, embedded in its group of permutations $B=Perm(G)$ via the left regular representation $\lambda:G\rightarrow B$, the normalizer of $\lambda(G)$ in $B$ is $\operatorname{Hol}(G)$, the holomorph of $G$. The set…

We study finite transitive permutation groups $G\leqslant\operatorname{Sym}(\Omega)$ such that all orbits of the conjugation action on $G$ of the normaliser of $G$ in $\operatorname{Sym}(\Omega)$ have size bounded by some constant. Our…

We investigate the group of normalized units of the group algebra $\mathbb{Z}_{p^e}G$ of a finite abelian $p$-group $G$ over the ring $\mathbb{Z}_{p^e}$ of residues modulo $p^e$ with $e\geq 1$.

If $\sigma$ is an automorphism of order $p$ of the semisimple group $\mathbf{G}$, there is a natural correspondence between mod $p$ cohomological automorphic forms on $\mathbf{G}$ and $\mathbf{G}^\sigma$. We describe this correspondence in…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

Recently George Bergman proved that the symmetric group of an infinite set possesses the following property which we call by the {\it universality of finite width}: given any generating set $X$ of the symmetric group of an infinite set…