Related papers: Free transport for interpolated free group factors
We consider the general $\mathbb{Z}_2$-symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and $\mathbb{Z}_n$-symmetric BBS $\tau^{(2)}$-model…
We discuss a partial normalisation of a finite graph of finite groups $(\Gamma(-), X)$ which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result, this provides a flexible and rather useful tool in the…
We introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free…
Free groups have many applications in Algebraic Topology. In this paper I specifically study the finitely generated free groups by using the covering spaces and fundamental groups. By the Van Kampen's theorem, we have a famous fact that the…
We give a general definition of classical and quantum groups whose representation theory is "determined by partitions" and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described…
We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki-Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann…
Let $\Free_n$ denote the free group with $n$ generators $g_1, g_2, ..., g_n$. Let $\lambda$ stand for the left regular representation of $\Free_n$ and let $\tau$ be the standard trace associated to $\lambda$. Given any positive integer $d$,…
Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath product. Then we discuss representation theory of free wreath products, with the…
We consider two extensions of free probability that have been studied in the research literature, and are based on the notions of c-freeness and respectively of infinitesimal freeness for noncommutative random variables. In a 2012 paper,…
Suppose $G$ is a free product $G = A_1 * A_2* \cdots * A_k * F_N$, where each of the groups $A_i$ is torsion-free and $F_N$ is a free group of rank $N$. Let $\mathcal{O}$ be the deformation space associated to this free product…
We present families of pairs of finite von Neumann algebras $A\subset M$ where $A$ is a maximal injective masa in the type $\mathrm{II}_1$ factor $M$ with separable predual. Our results make use of the strong mixing and the asymptotic…
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Fa\`a di Bruno algebra, and then to the group of a free operad over Schr\"oder trees. This leads to new combinatorial…
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…
In this paper we will give a similar factorization as in \cite{4}, \cite{5}, where the autors Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative…
Building on the previous extensive study of Yang, Gould and the present author, we provide a more precise insight into the group-theoretical ramifications of the word problem for free idempotent generated semigroups over finite biordered…
This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If $a_1,...,a_k$ are $\ast$-free $\mathscr{R}$-diagonal operators in a $\mathrm{II}_1$ factor, then $D_t(a_{i_1}...…
The free-fermion point refers to a $\operatorname{GL}(2)\times\operatorname{GL}(1)$ parametrized Yang-Baxter equation within the six-vertex model. It has been known for a long time that this is connected with the quantum group…
Let $\Gamma$ be a non-commutative free group on finitely many generators. In a previous work two of the authors have constructed the class of multiplicative representations of $\Gamma$ and proved them irreducible as representation of…
We extend the characterization of context-free groups of Muller and Schupp in two ways. We first show that for a quasi-transitive inverse graph $\Gamma$, being quasi-isometric to a tree, or context-free (finitely many end-cones types), or…
We explicitly write down the Eisenstein elements inside the space of modular symbols for Eisenstein series with integer coefficients for the congruence subgroups $\Gamma_0(N)$ with $N$ odd square-free. We also compute the winding elements…