Related papers: Calculation of a K_2 group of an F_2 coefficients …

Motivated by the search for new examples of "noncommutative manifolds", we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consier are the infinite dihedral group ${\bf Z}…

Let $\mathbb Z_n$ denote the cyclic group of order $n$. We show how the group determinant for $G= \mathbb Z_n \times H$ can be simply written in terms of the group determinant for $H$. We use this to get a complete description of the…

The partial group algebra of a group G over a field K, denoted by K_{par}(G), is the algebra whose representations correspond to the partial representations of G over K-vector spaces. In this paper we study the structure of the partial…

Let $\lambda$ be a primitive root of unity of order $\ell$. We introduce a family of finite-dimensional algebras $\{\mathcal{D}_{\lambda,N}(\mathfrak{sl}_2)\}_{N\in\mathbb{N}_0}$ over the complex numbers, such that…

Let $F$ be a field with at least three elements and $G$ a locally finite group. This paper aims to show that if either $F$ is algebraically closed or the characteristic of $F$ is positive, then an element in the group algebra $FG$ is a…

Odd index pairings of $K_1$-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a…

In this article I generalise previous computations (by K. Kato, T. Hara and myself) of K_1 (only up to p-power torsion) of p-adic group rings of finite non-abelian p-groups in terms of p-adic group rings of abelian subquotients of the…

We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with…

The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose…

Consider the abelian category $\mathcal{C}_k$ of commutative group schemes of finite type over a field $k$. By results of Serre and Oort, $\mathcal{C}_k$ has homological dimension $1$ (resp. $2$) if $k$ is algebraically closed of…

The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…

We present approaches for calculating the precise orders of the algebraic $K$-groups $K_{4n-2}(\mathcal{O}_K)$ for a totally real abelian $K$. Along the way, we also establish a formula connecting the order of $K_{4n-2}(\mathcal{O}_E)$ of a…

This paper is a report on a computer check of some positivity properties of the Hecke algebra in type H4, including the non-negativity of the coefficients of the structure constants in the Kazhdan-Lusztig basis. This answers a long-standing…

For a group $G$, N-series $\cal G$ of $G$ and commutative ring $R$ let $I^n_{R,\cal G}(G)$, $n\ge 0$, denote the filtration of the group algebra $R(G)$ induced by $\cal G$, and $I_R(G)$ its augmentation ideal. For subgroups $H$ of $G$, left…

For Artin groups of dihedral type, we compute the Bredon homology groups of the classifying space for the family of virtually cyclic subgroups with coefficients in the K-theory of a group ring.

A numerical semigroup $S$ is a cofinite, additively-closed subset of the nonnegative integers that contains $0$. In this paper, we initiate the study of atomic density, an asymptotic measure of the proportion of irreducible elements in a…

Let $\Delta$ be a numerical semigroup and let $d\ge 2$ be an integer. We study the fiber of the quotient map \(S\mapsto S/d\) over $\Delta$. We describe its elements as semigroups of the form $\langle X\rangle+d\Delta$, for suitable finite…

Let $\mathcal{O}_2$ and $\mathcal{O}'_2$ be two distinct finite local rings of length two with residue field of characteristic $p$. Let $\mathbb{G}(\mathcal{O}_2)$ and $\mathbb{G}(\mathcal{O}'_2)$, be the group of points of any reductive…

We determine the number of elements of order two in the group of normalized units V(F_2G) of the group algebra F_2G of a 2-group of maximal class over the field F_2 of two elements. As a consequence for the 2-groups G and H of maximal class…

Combinatorial curve neighborhoods are somewhat foundational when setting up the quantum Schubert calculus for affine flag manifolds. In the specific case of type $A_1^{(1)}$, you can encode these neighborhoods entirely within the moment…