Related papers: Projective Representations I. Projective lines ove…

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

In this note we establish the following result (announced in a previous work): if a linear group is the image of a representation of a K\"ahler group, then it has a finite index subgroup which is the image of a representation of the…

We give an explicit presentation with generators and relations of the quantum cohomology ring of the blow-up of a projective space along a linear subspace.

Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…

In analogy with the geometric situation, we study real calculi over projective modules and show that they can be realized as projections of free real calculi. Moreover, we consider real calculi over matrix algebras and discuss several…

Let $R$ be a commutative ring. We investigate $R$-modules which can be written as \emph{finite} sums of {\it {second}} $R$-submodules (we call them \emph{second representable}). We provide sufficient conditions for an $R$-module $M$ to be…

First we give a complex ball uniformization of the moduli space of 8 ordered points on the projective line by using the theory of periods of K3 surfaces. Next we give a projective model of this moduli space by using automorphic forms on a…

The projective representations of k-Galilei group G_k are found by contracting the relevant representations of k-Poincare group. The projective multiplier is found. It is shown that it is not possible to replace the projective…

Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…

The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…

In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a…

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring $\cR$, we prove…

This paper contains two results on the dimension and smoothness of radial projections of sets and measures in Euclidean spaces. To introduce the first one, assume that $E,K \subset \mathbb{R}^{2}$ are non-empty Borel sets with…

Let $(R,\mm,K)$ be a regular local ring containing a field $k$ such that either char $k=0$ or char $k=p$ and tr-deg $K/\BF_p\geq 1$. Let $g_1,\ldots,g_t$ be regular parameters of $R$ which are linearly independent modulo $\mm^2$. Let…

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

For a tensor ring $T_R(M)$, under certain conditions, we characterize the Gorenstein projective modules over $T_R(M)$, and prove that a $T_R(M)$-module $(X,u)$ is Gorenstein projective if and only if $u$ is monomorphic and ${\rm coker}(u)$…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…