相关论文: Strong asymptotic freeness for free orthogonal qua…
Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective…
We study the orthogonal quantum groups satisfying the ``easiness'' assumption axiomatized in our previous paper, with the construction of some new examples, and with some partial classification results. The conjectural conclusion is that…
We compute the Hochschild homology of the free orthogonal quantum group $A_o(n)$. We show that it satisfies Poincar\'e duality and should be considered to be a 3-dimensional object. We then use recent results of R. Vergnioux to derive…
We provide an informal introduction to tensor field theories and to their associated renormalization group. We focus more on the general motivations coming from quantum gravity than on the technical details. In particular we discuss how…
The study of the symmetry of Pais-Uhlenbeck oscillator initiated in [Nucl. Phys. B 885 (2014) 150] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck…
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we…
The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible…
Explicit convergence of suitably normalized integrals on balls where the integrand is the product of coefficients of the quasi-regular representation of the finitely generated free group.
Let $G$ be the group of automorphisms of a free group $F_\infty$ of infinite order. Let $H$ be the stabilizer of first $m$ generators of $F_\infty$. We show that the double cosets of $\Gamma$ with respect to $H$ admit a natural semigroup…
We show that, as n goes to infinity, the free group on n generators, modulo n+u random relations, converges to a random group that we give explicitly. This random group is a non-abelian version of the random abelian groups that feature in…
We give a criterion for a set of $n$ hyperbolic isometries of a $\mathrm{CAT}(0)$ metric space $X$ to generate a free group on $n$ generators. This extends a result by Alperin, Farb and Noskov who proved this for 2 generators under the…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…
In this paper we study the $ K $-theory of free quantum groups in the sense of Wang and Van Daele, more precisely, of free products of free unitary and free orthogonal quantum groups. We show that these quantum groups are $ K $-amenable and…
We construct a group (an HNN extension of a free group) with polynomial isoperimetric function, linear isodiametric function and non-simply connected asymptotic cones.
Previously one of us presented a conjecture [APF-4 Proceedings] to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of…
A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index,…
We discuss the classification problem for the unitary easy quantum groups, under strong axioms, of noncommutative geometric nature. Our main results concern the intermediate easy quantum groups $O_N\subset G\subset U_N^+$. To any such…
This is an introduction to the quantum groups, or rather to the simplest quantum groups. The idea is that the unitary group $U_N$ has a free analogue $U_N^+$, whose standard coordinates $u_{ij}\in C(U_N^+)$ are allowed to be free, and the…
We show that the reduced von Neumann algebras of the free orthogonal and free unitary quantum groups have the Haagerup approximation property. Using this result and a Haagerup-type inequality for these quantum groups due to Vergnioux (J.…
The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization…