Related papers: Construction of Spectral Triples Starting from Fre…

For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible…

We construct affine algebras with an arbitrary amount of simple modules of each dimension.

In this paper, we calculate the differential $d^1$ of the rank spectral sequence. We generalize Quillen's spectral sequence from Dedekind domain to general integral Noetherian ring $A$ by considering the Q-construction $Q^{tf}(A)$ of the…

This is the addendum to the paper "On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra" Communications in Algebra, 40:6 (2012), 2005-2036 (DOI: 10.1080/00927872.2011.570830). We give here the full proof of…

We discuss reflections identities of harmonic sums up to weight three. The need for this kind of identities emerges in analysis of the general structure of eigenvalue of the BFKL equation. The reflection identities decompose a product of…

Let $\mathbf{A} = (A_1,\ldots, A_q)$ be a $q$-tuple of finite sets of integers. Associated to every $q$-tuple of nonnegative integers $\mathbf{h} = (h_1,\ldots, h_q)$ is the linear form $\mathbf{h}\cdot \mathbf{A} = h_1 A_1 + \cdots +…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

We discuss some properties of the spectral triple $(A_F,H_F,D_F,J_F,\gamma_F)$ describing the internal space in the noncommutative geometry approach to the Standard Model, with $A_F=\mathbb{C}\oplus\mathbb{H}\oplus M_3(\mathbb{C})$. We show…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…

We consider four classes of polynomials over the fields $\mathbb{F}_{q^3}$, $q=p^h$, $p>3$, $f_1(x)=x^{q^2+q-1}+Ax^{q^2-q+1}+Bx$, $f_2(x)=x^{q^2+q-1}+Ax^{q^3-q^2+q}+Bx$, $f_3(x)=x^{q^2+q-1}+Ax^{q^2}-Bx$, $f_4(x)=x^{q^2+q-1}+Ax^{q}-Bx$,…

Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…

Given an expansive matrix $R\in M_d({\mathbb Z})$ and a finite set of digit $B$ taken from $ {\mathbb Z}^d/R({\mathbb Z}^d)$. It was shown previously that if we can find an $L$ such that $(R,B,L)$ forms a Hadamard triple, then the…

In this paper we introduce the family of spaces $RM(p,q)$, $1\leq p,q\leq +\infty$. They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when…

Let $\mathcal{G}$ denote the variety generated by infinite dimensional Grassmann algebras; i.e., the collection of all unitary associative algebras satisfying the identity $[[z_1,z_2],z_3]=0$, where $[z_i,z_j]=z_iz_j-z_jz_i$. Consider the…

We show that all triples $(x_1,x_2,x_3)$ of singular moduli satisfying $x_1 x_2 x_3 \in \mathbb{Q}^{\times}$ are "trivial". That is, either $x_1, x_2, x_3 \in \mathbb{Q}$; some $x_i \in \mathbb{Q}$ and the remaining $x_j, x_k$ are distinct,…

Let $p$ be an odd prime. For nontrivial proper subsets $A,B$ of $\mathbb{Z}_p$ of cardinality $s,t$, respectively, we count the number $r(A,B,B)$ of additive triples, namely elements of the form $(a, b, a+b)$ in $A \times B \times B$. For…

Let $p$ and $q$ be two positive primes. Let $\ell$ be an odd positive prime integer and $F$ a quadratic number field. Let $K$ be an extension of $F$ such that $K$ is a dihedral extension of $\Q$ of degree $\ell$ over $F$ or $K$ is an…

Let $X$ be a smooth projective curve over the complex numbers. To every representation $\rho\colon \GL(r)\lra \GL(V)$ of the complex general linear group on the finite dimensional complex vector space $V$ which satisfies the assumption that…

We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…

Let $(M,g)$ be an open, oriented and incomplete riemannian manifold of dimension $m$. Under some general conditions we show that it is possible to build a Hilbert complex $(L^2\Omega^i(M,g),d_{\mathfrak{M},i})$ such that its cohomology…