Related papers: Epic substructures and primitive positive function…

Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented…

Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $\alpha:=\{\alpha_x\}_{x \in…

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the…

Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3, or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group…

For a pair of finite relational structures $(\mathfrak{A},\mathfrak{B})$ such that $\mathfrak{A}$ homomorphically maps to $\mathfrak{B}$ we denote by $K_{(\mathfrak{A},\mathfrak{B})}$ the following statement: for all structures…

Let $\sR$ be an epireflective category of $\topo$ and let $F_\sR$\, be the epireflective functor associated with $\sR$. If $\sA$ denotes a (semi)topological algebraic subcategory of $\topo$, we study when $F_\sR\,(A)$ is an epireflective…

A subset $\mathcal{G}$ generating a $C^*$-algebra $A$ is said to be hyperrigid if for every faithful nondegenerate $*$-representation $A\subseteq B(H)$ and a sequence $\phi_n:B(H) \to B(H)$ of unital completely positive maps, we have that…

Given a connected dense Zariski open set of a compact K\"ahler manifold $U$, we address the general problem of the existence of surjective holomorphic maps ${F:U\to C}$ to smooth complex quasi-projective curves from properties of…

Let $\boldsymbol{G}$ be an algebraic group of exceptional Lie type in characteristic $p$, $G=\boldsymbol{G}^{\sigma}$ its fixed-point subgroup under the action of a Steinberg endomorphism $\sigma$, and $\overline{G}$ an almost simple group…

We show that algebraic analogues of universal group covers, surjective group homomorphisms from a $\mathbb{Q}$-vector space to $F^{\times}$ with "standard kernel", are determined up to isomorphism of the algebraic structure by the…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

We say that a finitely generated group $G$ has property (QT) if it acts isometrically on a finite product of quasi-trees so that orbit maps are quasi-isometric embeddings. A quasi-tree is a connected graph with path metric quasi-isometric…

Let $A$ be an integral $k$-algebra of finite type over an algebraically closed field $k$ of characteristic $p>0$. Given a collection ${\cal{D}}$ of $k$-derivations on $A$, that we interpret as algebraic vector fields on $X=Spec(A)$, we…

The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is…

Let X/S be a quasi-projective morphism over an affine base. We develop in this article a technique for proving the existence of closed subschemes H/S of X/S with various favorable properties. We offer several applications of this technique,…

This work is a continuation of Automorphisms of $K$-groups I, P. Flavell, preprint. The main object of study is a finite $K$-group $G$ that admits an elementary abelian group $A$ acting coprimely. For certain group theoretic properties…

A smooth complex variety satisfies the Generalized Jacobian Conjecture if all its \'etale endomorphisms are proper. We study the conjecture for $\mathbb{Q}$-acyclic surfaces of negative Kodaira dimension. We show that $G$-equivariant…

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a…

An almost PI algebra is a generalisation of a just infinite algebra which does not satisfy a polynomial identity. An almost PI algebra has some nice properties: It is prime, has a countable cofinal subset of ideals and when satisfying…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…