Related papers: Saturated free algebras revisited
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic…
We give some general theorems on free algebras of varieties of Boolean algebras with operators; a hitherto new result is obtained for Pinter's substitution algebras. For n\geq 3, and m>1, there is a generating set of the free algebra freely…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
The authors of this article intend to present some results obtained in the study of biderivations of complete Lie algebras. Firstly they present a matricial approach to do this, which was a useful and explanatory tool not only in the study…
Let $G$ be a finite group and $S$ a subset of $G$. Then $S$ is {\em product-free} if $S \cap SS = \emptyset$, and $S$ {\em fills} $G$ if $G^{\ast} \subseteq S \cup SS$. A product-free set is locally maximal if it is not contained in a…
This paper is the first in a sequence on the first order theory of free products. In the first paper we generalize the analysis of systems of equations over free and (torsion-free) hyperbolic groups, and analyze system of equations over…
Let $H \subseteq G$ be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic $p> 0$. In our first main theorem we show that if a closed subgroup $K$ of $H$ is $H$-completely reducible, then…
A brief introduction to universal algebra and the theory of topological algebras, their varieties, and free topological algebras is presented. Free topological Mal'tsev algebras are studied. Their properties, relationship with topological…
This note was originated many years ago as my reaction to questions of several people how free strongly homotopy algebras can be described and what can be said about the structure of the universal enveloping A(m)-algebra of an L(m)-algebra,…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
We develop an algorithm which, given a trained transformer model $\mathcal{M}$ as input, as well as a string of tokens $s$ of length $n_{fix}$ and an integer $n_{free}$, can generate a mathematical proof that $\mathcal{M}$ is…
Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the…
Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective amalgam $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. In the case where $ M_1 $…
The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…
Was paper 839 in the author's list until winter 2023 when it was divided into three. Part I: We would like to generalize imaginary elements, weight of ortp$(a,M,N), {\mathbf P}$-weight, ${\mathbf P}$-simple types, etc. from [She90, Ch.…
In this paper we construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence, we obtain free Hom-associative algebras generated by a set…