Related papers: The Chabauty-Kim Method for Relative Completions

The paper contains a generalization of known properties of Chebyshev polynomials of the second kind in one variable to polynomials of $n$ variables based on the root lattices of compact simple Lie groups $G$ of any type and of rank $n$. The…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is representable over a finite base. This result gives a positive…

Considering finite extensions K[A] \subseteq K[B] of positive affine semigroup rings over a field K we have developed in [1] an algorithm to decompose K[B] as a direct sum of monomial ideals in K[A]. By computing the regularity of…

Let $A$ be a symmetrizable generalized Cartan matrix, which is not of finite or affine type. Let $\mathfrak{g}$ be the corresponding Kac-Moody algebra over a commutative ring $R$ with $1$. We construct an infinite-dimensional group $G_V(R)$…

We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…

We establish vanishing results for the first cohomology group of nilpotent groups and Lie rings when the submodule of invariants is trivial. Our results are obtained within a model-theoretic setting, namely for structures that are definable…

We study the completion of a group relative to a Zariski dense representation in a reductive algebraic group over a field $k$. The characteristic zero case was worked out previously by R. Hain; we extend his results to arbitrary…

We present a method to explicitly compute a complete set of orthogonal primitive idempotents in a simple component with Schur index 1 of a rational group algebra $\mathbb{Q}G$ for $G$ a finite generalized strongly monomial group. For the…

Previous formulations of group theory in ACL2 and Nqthm, based on either "encapsulate" or "defn-sk", have been limited by their failure to provide a path to proof by induction on the order of a group, which is required for most interesting…

Loday's assembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalization that places both ingredients on the same footing. Building on…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

We study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and…

In this paper, our aim is twofold: First, by using the technique of gluing semigroups, we give infinitely many families of a projective closure with the Cohen-Macaulay (Gorenstein) property. Also, we give an effective technique for…

We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied…

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…