Related papers: Realization of permutation modules via Alexandroff…

Let $A$ be a finite-dimensional commutative associative algebra with unity over an algebraically closed field $\mathbb{K}$. The purpose of the paper is to study the solvability of $G_A$, where $G_A$ is the identity component of…

In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Marcus Reineke. Obtained is a generalization of this construction for finite dimensional associative algebras…

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…

Let $Y$ be a CW-complex with a single 0-cell, let $K$ be its Kan group, a free simplicial group whose realization is a model for the space $\Omega Y$ of based loops on $Y$, and let $G$ be a Lie group, not necessarily connected. By means of…

Let $G$ be a unimodular Lie group, $X$ a compact manifold with boundary, and $M$ the total space of a principal bundle $G\to M\to X$ so that $M$ is also a strongly pseudoconvex complex manifold. In this work, we show that if $G$ acts by…

The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…

For $n\ge5$, it is well known that the moduli space $\mathfrak{M_{0,\:n}}$ of unordered $n$ points on the Riemann sphere is a quotient space of the Zariski open set $K_n$ of $\mathbb C^{n-3}$ by an $S_n$ action. The stabilizers of this…

We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are…

We show that there are homotopy equivalences $h:N\to M$ between closed manifolds which are induced by cell-like maps $p:N\to X$ and $q:M\to X$ but which are not homotopic to homeomorphisms. The phenomenon is based on construction of…

We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space Bun(G) of G-bundles…

We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…

We investigate properties of finite transitive permutation groups $(G, \Omega)$ in which all proper subgroups of $G$ act intransitively on $\Omega.$ In particular, we are interested in reduction theorems for minimally transitive…

If $X$ is a variety with an additional structure $\xi$, such as a marked point, a divisor, a polarization, a group structure and so forth, then it is possible to study whether the pair $(X,\xi)$ is defined over the field of moduli. There…

The Modular Isomorphism Problem asks if an isomorphism of group algebras of two finite p-groups G and H over a field of characteristic p, implies an isomorhism of the groups G and H. We survey the history of the problem, explain strategies…

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

We describe a homotopy-theoretic approach to the theory of moduli of realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing a given $\Pi$-algebra as homotopy groups of a pointed space. Our techniques are based on…

Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for $G$ and the…

A saturated fusion system over a finite $p$-group $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over $S$ is realized…

A classical problem in the literature seeks the minimal number of proper subgroups whose union is a given finite group. A different question, with applications to error-correcting codes and graph colorings, involves covering vector spaces…

We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain…