Related papers: Semi-regular masas of transfinite length
Using methods of R.J.Tauer we exhibit an uncountable family of singular masas in the hyperfinite $\textrm{II}_1$ factor $\R$ all with Puk\'anszky invariant $\{1\}$, no pair of which are conjugate by an automorphism of $R$. This is done by…
We prove that any separable II$_1$ factor $M$ admits a {\it coarse decomposition} over the hyperfinite II$_1$ factor $R$, i.e., there exists an embedding $R\hookrightarrow M$ such that $L^2M\ominus L^2R$ is a multiple of the coarse Hilbert…
We investigate maximal abelian subalgebras (masas) in separably acting type $II_1$ factors. We use the notion of distance between masas which we introduced in an earlier paper in this archive, OA/0107075. The main result of the paper is to…
We construct numerous continuous families of irreducible subfactors of the hyperfinite II$_1$ factor, which are non-isomorphic, but have all the same standard invariant. In particular, we obtain 1-parameter families of irreducible,…
We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided…
In this paper, we give examples of maximal amenable subalgebras of the free group factor of two generators. More precisely, we consider two copies of the hyperfinite factor $R_i$ of type $\mathrm{II}_1$. From each $R_i$, we take a Haar…
Let $n$ be a positive integer and $\mathcal M$ a set of rational $n \times n$-matrices such that $\mathcal M$ generates a finite multiplicative semigroup. We show that any matrix in the semigroup is a product of matrices in $\mathcal M$…
We study a transfinite iteration of the ordinal Hessenberg natural sum obtained by taking suprema at limit stages and show that such an iterated natural sum differs from the more usual transfinite ordinal sum only for a finite number of…
We construct irreducible hyperfinite subfactors of index 6 with a prescribed fundamental group from a large family containing all countable and many uncountable subgroups of R_+. We also prove that there are unclassifiably many irreducible…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar…
An atomic monoid $M$ is called length-factorial if for every non-invertible element $x \in M$, no two distinct factorizations of $x$ into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The…
Let $G$ be a countable cancellative amenable semigroup and let $(F_n)$ be a (left) F{\o}lner sequence in $G$. We introduce the notion of an $(F_n)$-normal element of $\{0,1\}^G$. When $G$ = $(\mathbb N,+)$ and $F_n = \{1,2,...,n\}$, the…
In this paper, we construct invariant measures and global-in-time solutions for a fractional Schr\" odinger equation with a Moser-Trudinger type nonlinearity $$ i\partial_t u= (-\Delta)^{\alpha}u+ 2\beta u e^{\beta…
A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…
We study finite semigroups of $n \times n$ matrices with rational entries. Such semigroups provide a rich generalization of transition monoids of unambiguous (and, in particular, deterministic) finite automata. In this paper we determine…
For each sequence $\{c_n\}_n$ in $l_{1}(\N)$ we define an operator $A$ in the hyperfinite $\mathrm{II}_1$-factor $\mathcal{R}$. We prove that these operators are quasinilpotent and they generate the whole hyperfinite $\mathrm{II}_1$-factor.…
An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard…
Infinite time Turing machine models with tape length $\alpha$, denoted $T_\alpha$, strengthen the machines of Hamkins and Kidder [HL00] with tape length $\omega$. A new phenomenon is that for some countable ordinals $\alpha$, some cells…
We look at the long-time behaviour of solutions to a semi-classical Schr\"odinger equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the…