相关论文: Nearly all subspaces of a classical polar space ar…

We prove a generalization of the polarization identity of linear algebra expressing the inner product of a complex inner product space in terms of the norm, where the field of scalars is extended to an associative algebra equipped with an…

The topological symmetry group $\mathrm{TSG}(\Gamma)$ of an embedding $\Gamma$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,\Gamma)$. If we restrict to orientation…

Let $V$ be a simple vertex algebra of countable dimension, $G$ be a finite automorphism group of $V$ and $\sigma$ be a central element of $G$. Assume that ${\cal S}$ is a finite set of inequivalent irreducible $\sigma$-twisted $V$-modules…

Let $\Gamma$ be a finitely generated torsion-free group. We show that the statement of $\Gamma$ being virtually abelian is equivalent to the statement that the $*$-regular closure of the group ring $\mathbb{C}[\Gamma]$ in the algebra of…

Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective.…

We construct the most general four-dimensional ${\cal N}=4$ supergravity coupled to an arbitrary number $n$ of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of $\text{SL}(2,\mathbb{R}) \times…

This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

Let $G=PSL(2,\mathbb{R})$, let $\Gamma$ be a lattice in $G$, and let $\mathcal{H}$ be an irreducible unitary representation of $G$ with square-integrable matrix coefficients. A theorem in [Goodman, de la Harpe, Jones 1989] states that the…

A point set $S \subseteq \mathbb{R}^2$ is universal for a class $\cal G$ if every graph of ${\cal G}$ has a planar straight-line embedding on $S$. It is well-known that the integer grid is a quadratic-size universal point set for planar…

Let $G$ be a finite group. Let $\sigma =\{\sigma_{i} | i\in I\}$ be a partition of the set of all primes $\Bbb{P}$ and $n$ an integer. We write $\sigma (n) =\{\sigma_{i} |\sigma_{i}\cap \pi (n)\ne \emptyset \}$, $\sigma (G) =\sigma (|G|)$.…

For a fixed mod $p$ automorphic Galois representation, $p$-adic automorphic Galois representations lifting it determine points in universal deformation space. In the case of modular forms and under some technical conditions, B\"{o}ckle…

For an index set $\Gamma$ and a cardinal number $\kappa$ the $\Sigma_{\kappa}$-product of real lines $\Sigma_{\kappa}(\mathbb{R}^{\Gamma})$ consist of all elements of $\mathbb{R}^{\Gamma}$ with $<\kappa$ nonzero coordinates. A compact space…

We consider a class K of structures e.g. trees with omega +1 levels, metric spaces and mainly, classes of Abelian groups like the one mentioned in the title and the class of reduced separable (Abelian) p-groups. We say M in K is universal…

Let $F$ be a global field, $A$ a central simple algebra over $F$ and $K$ a finite (separable or not) field extension of $F$ with degree $[K:F]$ dividing the degree of $A$ over $F$. An embedding of $K$ in $A$ over $F$ exists implies an…

The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being zero-dimensional affine subspaces, and the usual Grassmannian, linear subspaces being special cases of affine subspaces. We show…

The set of all artin level quotients of a polynomial algebra in n variables having specified socle degree and type admits a parameter space. It is in fact a quasiprojective variety, naturally embedded in a Grassmannian. We give a geometric…

Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…

We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…

We use the Schwarz-Christoffel formula to show that for every $n\geq 3$, the space of labelled immersed $n$-gons in the plane up to similarity is homeomorphic to $\mathbb{R}^{2n-4}$. We then prove that all immersed triangles,…