Related papers: On $\mathcal A$-Transvections and Symplectic $\mat…

Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive…

Let $f$ be a newform of weight $2$, square-free level and trivial character, let $A_f$ be the abelian variety attached to $f$ and for every good ordinary prime $p$ for $f$ let $\boldsymbol f^{(p)}$ be the $p$-adic Hida family through $f$.…

We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \stackrel{f_1}{\rightarrow} M_1…

We investigate the question of when free structures of infinite rank (in a variety) possess model-theoretic properties like categoricity in higher power, saturation, or universality. Concentrating on left $R$-modules we show, among other…

In this article, we prove commutativity principal for linear, symplectic and transvection groups. This principle is a consequence of Quillen-Suslin local global principle and using a non-symmetric application of it as done by A. Bak. The…

We study valued fields equipped with an automorphism $\sigma$ which is locally infinitely contracting in the sense that $\alpha\ll\sigma\alpha$ for all $0<\alpha\in\Gamma$. We show that various notions of valuation theory, such as Henselian…

Let G be a connected reductive group. In this paper we are studying the invariant theory of symplectic G-modules. Our main result is that the invariant moment map is equidimensional. We deduce that the categorical quotient is a fibration…

Minimal Cantor systems of finite topological rank (that can be represented by a Bratteli-Vershik diagram with a uniformly bounded number of vertices per level) are known to have dynamical rigidity properties. We establish that such systems,…

Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our…

We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $H\le…

Suppose $T$ is totally transcendental and every minimal non-locally-modular type is nonorthogonal to a nonisolated minimal type over the empty set. It is shown that a finite rank type $p=tp(a/A)$ is isolated if and only if $a$ is…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

Let M be the cotangent bundle of S^2, with the standard symplectic structure. By adapting an argument of Gromov we determine the weak homotopy type of the group S of those symplectic automorphisms of M which are trivial at infinity. It…

Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0.…

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the…

We describe the structure of the Lie groups endowed with a left-invariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This…

We complete the list of normal forms for effective 3-forms with constant coefficients with respect to the natural action of symplectomorphisms in \mathbb{R}^6. We show that the 3-form which corresponds to the Special Lagrangian equation is…

We study subsets in possibly degenerate symplectic vector spaces over finite fields, which are stable under a given Coxeter/Weyl reflection group. These symplectic root systems provide crucial combinatorical data to classify…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

Let $M$ be a compact orientable surface equipped with a volume form $\omega$, $P$ be either $\mathbb{R}$ or $S^1$, $f:M\to P$ be a $C^{\infty}$ Morse map, and $H$ be the Hamiltonian vector field of $f$ with respect to $\omega$. Let also…