Related papers: Essential p-dimension of algebraic groups whose co…

In the present notes we provide a new uniform way to compute a canonical p-dimension of a split algebraic group G for a torsion prime p using degrees of basic polynomial invariants described by V.Kac. As an application, we compute the…

The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that…

One of the important open problems in the theory of central simple algebras is to compute the essential dimension of $\operatorname{GL}_n/\mu_m$, i.e., the essential dimension of a generic division algebra of degree $n$ and exponent…

In this paper, we compute the essential $p$-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, specifically the quasi-simple groups arising from the general linear and special linear groups, the…

Let G be a connected, adjoint, simple algebraic group over the complex numbers with a maximal torus T and a Borel subgroup B containing T. The study of zero weight spaces in irreducible representations of G has been a topic of considerable…

In this paper, we compute the fundamental group of the complement of linear torus curves of maximal contact and we show that it is isomorphic that of generic linear torus curves.

We consider two non-degenerate potentials for the quiver arising from the once-punctured torus, which are a natural choice to study and compare: the first is the Labardini-potential, yielding a finite-dimensional Jacobian algebra, whereas…

This paper is devoted to the study of topological quotients of compact linear Lie groups. More precisely, it investigates the question of when such a quotient is a topological or a smooth manifold. The topological quotient of a finite…

If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results…

Let $k$ be an algebraically closed field of characteristic 0, $Y=k^{r}\times {(k^{\times})}^{s}$ and let $G$ be an algebraic torus acting diagonally on the ring of differential operators $\cD (Y)^G$. We give necessary and sufficient…

Suppose $G$ is a finite group and $p$ is either a prime number or $0$. For $p$ positive, we say that $G$ is weakly tame at $p$ if $G$ has no non-trivial normal $p$-subgroups. By convention we say that every finite group is weakly tame at…

We characterize the rank of edge connection matrices of partition functions of real vertex models, as the dimension of the homogeneous components of the algebra of $G$-invariant tensors. Here $G$ is the sub- group of the real orthogonal…

We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded…

This work is concerned with the calculation of the fundamental group of torus knots. Torus knots are special types of knots which wind around a torus a number of times in the longitudinal and meridional directions. We compute and describe…

We describe a unified approach to estimating the dimension of $f^{-1}(A)$ for any $G$-equivariant map $f \colon X \to Y$ and any closed $G$-invariant subset $A\subseteq Y$ in terms of connectivity of $X$ and dimension of $Y$, where $G$ is…

Given a connected algebraic group G over an algebraically closed field and a G-homogeneous space X, we describe the Chow ring of G and the rational Chow ring of X, with special attention to the Picard group. Also, we investigate the…

Consider the algebraic function $\Phi_{g,n}$ that assigns to a general $g$-dimensional abelian variety an $n$-torsion point. A question first posed by Kronecker and Klein asks: What is the minimal $d$ such that, after a rational change of…

We define and study the essential dimension of an algebraic stack. We compute the essential dimension of the stacks Mgn and MgnBar of smooth, or stable, n-pointed curves of genus g. We also prove a general lower bound for the essential…

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of…

In this paper the space of commuting elements in the central product $G_{m,p}$ of $m$ copies of the special unitary group $SU(p)$ is studied, where $p$ is a prime number. In particular, a computation for the number of path connected…