Related papers: Bounded normal generation for projective unitary g…
We give a complete description of the bounded (i.e. norm continuous) unitary representations of the Fr\'echet-Lie algebra of all smooth sections, as well as of the LF-Lie algebra of compactly supported smooth sections, of a smooth Lie…
The irreducible representations of SU(N) over a mixed quark-antiquark Fock space component have been studied for many years. In analogy to the case for the quark-only Fock space component, there exist efficient tools to classify the…
The existence of $1$-factorizations of an infinite complete equipartite graph $K_m[n]$ (with $m$ parts of size $n$) admitting a vertex-regular automorphism group $G$ is known only when $n=1$ and $m$ is countable (that is, for countable…
We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…
Following partially a suggestion by Pyber, we prove that the diameter of a product of non-abelian finite simple groups is bounded linearly by the maximum diameter of its factors. For completeness, we include the case of abelian factors and…
We investigate the structure of crossed product von Neumann algebras arising from Bogoljubov actions of countable groups on Shlyakhtenko's free Araki-Woods factors. Among other results, we settle the questions of factoriality and Connes'…
Let $R$ be the hyperfinite ${\rm II}_1$ factor and let $u,v$ be two generators of $R$ such that $u^*u=v^*v=1$ and $vu=e^{2\pi i\theta} uv$ for an irrational number $\theta$. In this paper we study the class of operators $uf(v)$, where $f$…
Let $A$ be a commutative ring, and assume every non-trivial ideal of $A$ has finite-index. We show that if ${\rm{SL}}_n(A)$ has bounded elementary generation then every conjugation-invariant norm on it is either discrete or precompact. If…
We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
We present a development in the computational suite for the study of $N_\infty$ operads for a finite group $G$. This progress is achieved using the simple yet powerful observation that Rubin's generation algorithm can be interpreted as a…
We prove rigidity properties for von Neumann algebraic graph products. We introduce the notion of rigid graphs and define a class of II$_1$-factors named $\mathcal{C}_{\rm Rigid}$. For von Neumann algebras in this class we show a unique…
A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from $1947$ is uniform simplicity. A group $G$ is said to be $n$-uniformly simple for $n \in \mathbf{N}$ if for every $f,g\in G\setminus \{id\}$,…
For two ideals $I$ and $J$ of a noetherian ring, we characterize, in terms of the vanishing of Tor modules, when the associated graded ring of the sum $I+J$ is isomorphic to the tensor product of the associated graded ring of $I$ and the…
Let $\Sigma$ be a surface with negative Euler characteristic, genus at least one and at most one boundary component. We prove that the skein algebra of $\Sigma$ over the field of rational functions can be algebraically generated by a finite…
We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated…
In this article, we proved the following results. Let $L(F(n_i))$ be the free group factor on $n_i$ generators and $\lambda (g_{i})$ be one of standard generators of $L(F(n_i))$ for $1\le i\le N$. Let $\A_i$ be the abelian von Neumann…
It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties,…
Given a Hilbert space and the generator $A$ of a strongly continuous, exponentially stable, semigroup on this Hilbert space. For any $g(-s) \in {\mathcal H}_{\infty}$ we show that there exists an infinite-time admissible output operator…