Related papers: The Twisted Derivation Problem for Group Rings

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…

Given a $1$-tilting cotorsion pair over a commutative ring, we characterise the rings over which the $1$-tilting class is an enveloping class. To do so, we consider the faithful finitely generated Gabriel topology $\mathcal{G}$ associated…

In this paper we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes - under certain conditions - the bounded derived…

Given a discrete group $\G$ and an orthogonal action $\gamma: \G \to O(n)$ we study $L_p$ convergence of Fourier integrals which are frequency supported on the semidirect product $\R^n \rtimes_\gamma \G$. Given a unit $u \in \R^n$ and $1 <…

Suppose, $G$ is a residually finite group of finite upper rank admitting an automorphism $\varphi$ with finite Reidemeister number $R(\varphi)$ (the number of $\varphi$-twisted conjugacy classes). We prove that such $G$ is soluble-by-finite…

H.J. Zassenhaus conjectured that any unit of finite order and augmentation $1$ in the integral group ring $\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra $\mathbb{Q}G$ to an element of $G$. We prove the…

Let $G$ be a group and let $R$ be a $G$-graded ring. We show that a nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain…

Given a double cover $\pi: \mathcal{G} \rightarrow \hat{\mathcal{G}}$ of finite groupoids, we explicitly construct twisted loop transgression maps, $\tau_{\pi}$ and $\tau_{\pi}^{ref}$, thereby associating to a Jandl $n$-gerbe…

This paper is devoted to derivations in bimodules over group rings using previously proposed methods which are related to character spaces over groupoids. The theorem describing the arising spaces of derivations is proved. We consider some…

Invertibility is important in ring theory because it enables division and facilitates solving equations. Moreover, (nonassociative) rings can be endowed with an extra ''structure'' such as order and topology allowing more richness in the…

We study discrete torsion for the $n$--torus with finite symmetry group $G$ from the Dijkgraaf--Witten viewpoint. A class in $H^n(G,U(1))$ assigns a phase to each flat $G$--bundle, equivalently to each commuting $n$--tuple in $G$ up to…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of \v{C}esnavi\v{c}ius and Fedorov, we prove a non-noetherian…

We study the derived tensor product of the representation rings of subgroups of a given compact Lie group G. That is, given two such subgroups H_1 and H_2, we study the tensor product of the associated representation rings R(H_1) and R(H_2)…

Given an ample Hausdorff groupoid $G$, a unital commutative ring $R$, and a discrete twist $(\Sigma,i,q)$, we establish a generalised uniqueness theorem for the twisted Steinberg algebra $A_R(G;\Sigma)$. By applying this theorem when $G$ is…

For any commutative ring $A$ we introduce a generalization of $S$-noetherian rings using a hereditary torsion theory $\sigma$ instead of a multiplicatively closed subset $S\subseteq{A}$. It is proved that if $A$ is a totally…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

Let $H$ be a finite dimensional pointed rank one Hopf algebra of nilpotent type. We first determine all finite dimensional indecomposable $H$-modules up to isomorphism, and then establish the Clebsch-Gordan formulas for the decompositions…

We study an abstract group of reversible Turing machines. In our model, each machine is interpreted as a homeomorphism over a space which represents a tape filled with symbols and a head carrying a state. These homeomorphisms can only…

Let $G$ be a connected semisimple Lie group with its maximal compact subgroup $K$ being simply-connected. We show that the twisted equivariant $KK$-theory $KK^{\bullet}_{G}(G/K, \tau_G^G)$ of $G$ has a ring structure induced from the…

In this article, we prove that if $H$ is a skew field of center $k$ and $\sigma$ an automorphism of finite order of $H$ such that the fixed subfield $k^{\langle \sigma \rangle}$ of $k$ under the action of $\sigma$ contains an ample field,…