Related papers: On algebraic group varieties
Regular algebraic surfaces isogenous to a higher product of curves can be obtained from finite groups with ramification structures. We find unmixed ramification structures for finite groups constructed as p-quotients of particular infinite…
We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important…
We explore connected affine algebraic groups $G$, which enjoy the following finiteness property $\rm (F)$: for every algebraic action of $G$, the closure of every $G$-orbit contains only finitely many $G$-orbits. We obtain two main results.…
We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) on an affine scheme $X$ over $k$, then the dur sheaf $X\tilde{\tilde{/}}G$ of…
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This allows us to completely classify topological isomorphism…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.
We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$. We produce partial results for abelian varieties over a general finite…
We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…
We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is…
We investigate flexibility of affine varieties with an action of a linear algebraic group. Flexibility of a smooth affine variety with only constant invertible functions and a locally transitive action of a reductive group is proved. Also…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.
We obtain some new results on products of large and small sets in the Heisenberg group as well as in the affine group over the prime field. Also, we derive an application of these growth results to Freiman's isomorphism in nonabelian…
We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field of arbitrary characteristic, generalizing some results of Gaitsgory and showing that this category…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We classify finite groups $G$, such that the group algebra, $\mathbb{Q}G$ (over the field of rational numbers $\mathbb{Q}$), is the direct product of the group algebra $\mathbb{Q}[G/N]$ of a proper factor group $G/N$, and some division…
In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.