Related papers: Enumerating limit groups: A Corrigendum

It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples…

In the knowledge engineering community "ontology" is usually defined in the tradition of Gruber as an "explicit specification of a conceptualization". Several variations of this definition exist. In the paper we argue that (with one notable…

We show that the recently-introduced formalism by Neuhauser et al. for the calculation of the quasi-particle energies of electronic systems within the framework of the GW approximation of the self-energy operator, named the `stochastic GW…

The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies,…

The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…

We restrict the type of $2 \times 2$-matrices which can occur as simple components in the Wedderburn decomposition of the rational group algebra of a finite group. This results in a description up to commensurability of the group of units…

I correct two misapprehensions, one historical and one conceptual, in the recent literature on extensions of the Wigner's Friend thought-experiment. Perhaps fittingly, both concern the accurate description of some quantum physicists'…

We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has…

Let $\mathbb {F}_q$ be a finite field and $G$ a finte group with $(|G|,q)=1$. By a group code in $\mathbb {F}_q[G]$ we mean a two-sided ideal in $\mathbb {F}_q[G]$. We will prove a general criterion for the existence of group codes with…

Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any…

We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…

Quasigroup equational definitions are given.

We prove that the set of limit groups is recursive, answering a question of Delzant. One ingredient of the proof is the observation that a finitely presented group with local retractions (a la Long and Reid) is coherent and, furthermore,…

We survey the known results regarding the boundaries of word-hyperbolic groups.

A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a…

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear…

The aim of this paper is to reformulate the theory of unbounded derived categories, including more recent categories of first and second kind, using the language of $(\infty,1)$-categories.

We show that any finite group $G$ there exists a bijction $f$ from $G$ onto $C_{n}$ such that $o(x)$ divides $o(f(x))$ for all $x\in G$. This confirm Problem 18.1 in [7].

We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights in \cited{To}.

If $G$ is a Chevalley group and $R$ is an adele ring, or a product of local factors in an adele ring, then $R$ is bi-interpretable with $G(R)$.