相关论文: Pure eigenstates for the sum of generators of the …

We analyze the structure of left maps in algebraic weak factorization systems constructed using Garner's algebraic small object argument. We find that any left map can be constructed from generators in Bourke and Garner's double category of…

Let (G,S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C-*-algebra of G is simple with unique normalised…

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a…

We prove that the pure state space is homogeneous under the action of the group of asymptotically inner automorphisms for all the separable simple nuclear C*-algebras. If simplicity is not assumed for the C*-algebras, the set of pure states…

We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…

We show that any countable subgroup of the multiplicative group $\mathbb{R}_+^{\times}$ of positive real numbers can be realized as the fundamental group $\mathcal{F}(A)$ of a separable simple unital $C^*$-algebra $A$ with unique trace.…

We give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive…

We discuss the martingales in relevance with $G$-strongly quasi-invariant states on a $C^*$-algebra $\mathcal A$, where $G$ is a separable locally compact group of $*$-automorphisms of $\mathcal A$. In the von Neumann algebra $\mathfrak A$…

We prove that the word problem of a finitely generated group $G$ is in NP (solvable in polynomial time by a non-deterministic Turing machine) if and only if this group is a subgroup of a finitely presented group $H$ with polynomial…

It was recently shown that each C*-algebra generated by a faithful irreducible representation of a finitely generated, torsion free nilpotent group is classified by its ordered K-theory. For the three step nilpotent group $UT(4,\mathbb{Z})$…

Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This is based on a new proof of the result (in more general form…

We show that if $H \leq G$ is a closed amenable and cocompact subgroup of a unimodular locally compact group, then the reduced group C*-algebra of $G$ is not simple. Equivalently, there are unitary representations of $G$ that are weakly…

We consider space functions $s(n)$ of finitely presented groups $G =< A\mid R> .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use…

Let $\mathbb{G}$ be the quantum automorphism group of a finite dimensional C*-algebra $(B,\psi)$ and $\Gamma$ a discrete group. We want to compute the fusion rules of $\widehat{\Gamma}\wr_* \mathbb{G}$. First of all, we will revise the…

We propose to study some properties of the $C^*$-algebra naturally built out of the fundamental action that an automaton group $G$ admits on a regular rooted trees $\tree$.

We introduce the notion of weakly (strongly) infinite real rank for unital $C^{\ast}$-algebras. It is shown that a compact space $X$ is weakly (strongly) infine-dimensional if and only if $C(X)$ has weakly (strongly) infinite real rank.…

If the free algebra F on one generator in a variety V of algebras (in the sense of universal algebra) has a subalgebra free on two generators, must it also have a subalgebra free on three generators? In general, no; but yes if F generates…

We show that if a finite dimensional Hopf algebra over ${\bf C}$ has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group $G$ and a factorization $G=G_+G_-$ into two…

There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…

Given a locally compact quantum group $\mathbb G$, we define and study representations and C$^\ast$-completions of the convolution algebra $L_1(\mathbb G)$ associated with various linear subspaces of the multiplier algebra $C_b(\mathbb G)$.…