Related papers: On the notion of lower central series for loops
We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
Let $R$ be a graded ring. We introduce a class of graded $R$-modules called Gr\"obner-coherent modules. Roughly, these are graded $R$-modules that are coherent as ungraded modules because they admit an adequate theory of Gr\"obner bases.…
We show that the commensurator of any finitely generated abelian subgroup $H$ in a biautomatic group centralises a finite-index subgroup of $H$. We deduce that the CAT(0) groups introduced by Leary-Minasyan are either biautomatic or cannot…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
In this paper we present a unified proof of the fact that the category of modules over a ring and the category of near-vector spaces in the sense of J. Andr\'e, over an appropriate scalar system (a 'scalar group'), are both abelian…
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…
It is well known that the classical diagram lemmas of homological algebra for abelian groups can be generalized to non-abelian group-like structures, such as groups, rings, algebras, loops, etc. In this paper we establish such a…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of "connection" as a new kind of degeneracy. In this paper, for a cubical set with connections, we show that the connections generate an acyclic…
This paper continues the study of the lower central series quotients of an associative algebra A, regarded as a Lie algebra, which was started in math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second quotient in…
Our focus is on the set of lower-triangular, infinite matrices that have natural operations like addition, multiplication by a number, and matrix multiplication. With respect to addition this set forms and abelian group while with respect…
We introduce the universal unitarily graded A-algebra for a commutative ring A and an arbitrary abelian extension U of the group of units of A, and use this concept to give simplified proofs of the main theorems of co-Galois theory in the…
The {\em abeliant} is a polynomial rule for producing an $n$ by $n$ matrix with entries in a given ring from an $n$ by $n$ by $n+2$ array of elements of that ring. The theory of abeliants, first introduced in an earlier paper of the author,…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
We give a local characterization for when certain quiver representations in semisimple Abelian categories are semisimple, among them those arising from degenerations of linear series. This paper is the first of two, aimed to describe all…