Related papers: Rational series in the free group and the Connes o…
We give a description of operator algebras of free wreath products in terms of fundamental algebras of graphs of operator algebras as well as an explicit formula for the Haar state. This allows us to deduce stability properties for certain…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
We argue that an imperfect criminal law procedure cannot be group-fair, if 'group fairness' involves ensuring the same chances of acquittal or convictions to all innocent defendants independently of their morally arbitrary features. We show…
Hrube\v{s} and Wigderson [HW14] initiated the study of noncommutative arithmetic circuits with division computing a noncommutative rational function in the free skew field, and raised the question of rational identity testing. It is now…
We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let $p$ be an operator-valued polynomial in $B(H)\otimes C<x>$ of degree at most $2d+1$, where $H$ is…
Accessible groups for which the language of all words defining the identity is accepted by a certain class of nested stack automata are virtually free.
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a…
We introduce the notion of a bounded weight function on a language, and show that the set of bounded weight functions on a regular language is a rational polyhedral cone. We study the cell recognised by a bounded weight function (that is,…
We study stable commutator length (scl) in free products via surface maps into a wedge of spaces. We prove that scl is piecewise rational linear if it vanishes on each factor of the free product, generalizing the main result in Danny…
We re-cast in a more combinatorial and computational form the foldings approach of John Stallings and pursue a detailed study of the subgroup structure of free groups. In particular, we introduce the notions of an "algebraic" and a "free"…
In this work, the author gives a character-free proof of the Frobenius theorem. The new proof is based on some notions and results from the theory of ternary operations, the theory of orthogonal binary operations, the theory of transversals…
The classical theory of free analysis generalizes the noncommutative (nc) polynomials and rational functions, easily providing such results as an nc analogue of the Jacobian conjecture. However, the classical theory misses out on important…
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…
We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy…
In this paper, we work on the pro-nilpotent group topology of a free group. First we investigate the closure of the product of finitely many subgroups of a free group in the pro-nilpotent group topology. We present an algorithm for the…
We present a new approach to cyclic homology that does not involve the Connes differential and is based on a `noncommutative equivariant de Rham complex' of an associative algebra. The differential in that complex is a sum of the Karoubi-de…
We give a suitable definition of the concept of rational complex and prove that every rational exponential group is the fundamental group of some such a complex. In this framework, we prove that the variety of rational exponential groups is…
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…
Let $\mathbb Z_n$ be the cyclic group of order $n \ge 3$ additively written. S. Savchev \& F. Chen (2007) proved that for each zero-sum free sequence $S = a_1 \bullet \dots \bullet a_t$ over $\mathbb Z_n$ of length $t > n/2$, there is an…