相关论文: Tight decomposition of factors and the single gene…

We show that finitely generated irreducible $\mathrm{II}_1$ subfactors are generic in the following sense. Given a separable $\mathrm{II}_1$ factor $M$ and an integer $n\geq 2$, equip the set of $n$-tuples of self-adjoint operators in $M$…

Given a simple vertex algebra A and a reductive group G of automorphisms of A, the invariant subalgebra A^G is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally not true…

For a right-angled Coxeter system $(W,S)$ and $q>0$, let $\mathcal{M}_q$ be the associated Hecke von Neumann algebra, which is generated by self-adjoint operators $T_s, s \in S$ satisfying the Hecke relation $(\sqrt{q}\: T_s - q) (\sqrt{q}…

We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years. We discuss the appropriate first-order language for axiomatizing this class as well as the subclass of II$_1$…

For every $n\in \mathbb{N}$ we obtain a separable II$_1$ factor $M$ and a maximally abelian subalgebra $A\subset M$ such that the space of maximally amenable extensions of $A$ in $M$ is affinely identified with the $n$ dimensional…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture…

We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a…

For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial…

A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…

We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant $\Lambda_{\cb}(\Gamma) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(\Gamma)$ are strongly solid, i.e. the…

Class-S theories are four-dimensional N=2 supersymmetric field theories constructed by the reduction of a (2,0) six-dimensional theory on a punctured Riemann surface C (called the UV curve). A basic degeneration limit of the surface C is…

A discrete subset $S$ of a topologically gyrogroup $G$ is called a {\it suitable set} for $G$ if $S\cup \{1\}$ is closed and the subgyrogroup generated by $S$ is dense in $G$, where $1$ is the identity element of $G$. In this paper, we…

We use continuous model theory to obtain several results concerning isomorphisms and embeddings between II_1 factors and their ultrapowers. Among other things, we show that for any II_1 factor M, there are continuum many nonisomorphic…

We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X->B with singular fibre over b_0 \in B yields a family M(X/B,\beta) -> B of moduli stacks of stable…

A superconnection is a supermatrix whose even part contains the gauge-potential one-forms of a local gauge group, while the odd parts contain the (0-form) Higgs fields; the combined grading is thus odd everywhere. We demonstrate that the…

Given a II$_1$ factor $M$, a W$^*$-subalgebra $Q\subset M$ is {\it compressible} if for any $\varepsilon>0$ there exists a finite set of unitary elements $\Cal U_0\subset \Cal U(M)$ such that $\| \frac{1}{|\Cal U_0|}\sum_{u\in \Cal U_0}…

We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras $M_1 \ast_B M_2$ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free…

We single out a large class of groups ${\mathscr{M}}$ for which the following unique prime factorization result holds: if $\Gamma_1,\dots,\Gamma_n\in {\mathscr{M}}$ and $\Gamma_1\times\dots\times\Gamma_n$ is measure equivalent to a product…

In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…