Related papers: Schofield sequences in the Euclidean case

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…

Let $X$ be a complex surface obtained as the quotient of the complex Euclidean space $\mathbb{C}^2$ by a discrete subgroup of rank $3$. We investigate the cohomology group $H_0^1(X, E)$ with compact support for a unitary flat line bundle…

We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…

Let $p$ be an odd prime and let $\mathbf{B}$ be a $p$-block of a finite group, such that $\mathbf{B}$ has cyclic defect groups. We describe the self-dual indecomposable $\mathbf{B}$-modules and for each such module determine whether it is…

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other.…

Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $\varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic…

We prove that a simple knot in the lens space $L(p,q)$ fibers if and only if its order in homology does not divide any remainder occurring in the Euclidean algorithm applied to the pair $(p,q)$. One corollary is that if $p=m^2$ is a perfect…

A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections…

Elements of the Riordan group $\cal R$ over a field $\mathbb F$ of characteristic zero are infinite lower triangular matrices which are defined in terms of pairs of formal power series. We wish to bring to the forefront, as a tool in the…

For an inverse semigroup S with the set of idempotents E and a minimal idempotent, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat, or…

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${}…

In this paper we study Category $\mcal O$ for the polynomial toroidal Lie algebras and its $S,H$ type subalgebras. We classify irreducible objects of category $\mcal O$ as unique irreducble quotient of standard modules. Surprisingly,…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

The idea that the cohomology of finite groups might be fruitfully approached via the cohomology of ambient semisimple algebraic groups was first shown to be viable in the papers [CPS75] and [CPSvdK77]. The second paper introduced, through a…

Given $\mathbb{F}_{q^{n}}$, a field with $q^n$ elements, where $q $ is a prime power and $n$ is positive integer. For $r_1,r_2,m_1,m_2 \in \mathbb{N}$, $k_1,k_2 \in \mathbb{N}\cup \{0\}$, a rational function $F = \frac{F_1}{F_2}$ in…

Let $\mathcal{J}$ be the exceptional Jordan algebra and $V=\mathcal{J}\oplus \mathcal{J}$. We construct an equivariant map from $V$ to $\mathrm{Hom}_k(\mathcal{J}\otimes \mathcal{J},\mathcal{J})$ defined by homogeneous polynomials of degree…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

This paper presents some results on simple exceptional Jordan algebra over algebraically closed field $\Phi$ with characteristic not 2. Namely an example of simple decomposition of $H(O_3)$ into the sum of two subalgebras of the type…

Let $\mathfrak{g} = \mathfrak{g}_{\overline{0}} \oplus \mathfrak{g}_{\overline{1}}$ be a Lie superalgebra over an algebraically closed field, $k$, of characteristic 0. An endotrivial $\mathfrak{g}$-module, $M$, is a…

Let $\mathcal{O}_K$ be the ring of integers of an algebraic number field $K$ embedded into $\mathbb{C}$. Let $X$ be a subset of the Euclidean space $\mathbb{R}^d$, and $D(X)$ be the set of the squared distances of two distinct points in…