Related papers: Heat semigroups on quantum automorphism groups of …

In this paper we study two semigroups of completely positive unital self-adjoint maps on the von Neumann algebras of the free orthogonal quantum group $O_N^+$ and the free permutation quantum group $S_N^+$. We show that these semigroups…

In sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they…

Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and string theory. The typical construction of an automorphic heat…

We consider a quantum generalization of the classical heat equation, and study contractivity properties of its associated semigroup. We prove a Nash inequality and a logarithmic Sobolev inequality. The former leads to an ultracontractivity…

In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities on graphs. We also show that under the assumption of volume…

We compute the $ K $-theory of quantum automorphism groups of finite dimensional $ C^* $-algebras in the sense of Wang. The results show in particular that the $ C^* $-algebras of functions on the quantum permutation groups $ S_n^+ $ are…

We establish sharp Sobolev embedding properties within a broad class of compact matrix quantum groups of Kac type under the polynomial growth or the rapid decay property of their duals. Main examples are duals of polynomially growing…

We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as…

The heat semigroup on discrete hypercubes is well-known to be contractive over $L_p$-spaces for $1<p<\infty$. A question of Mendel and Naor \cite{MN14} concerns a stronger contraction property in the tail spaces, which is known as the…

The main goal of this paper is to generalize the Sobolev-type inequalities given by Guo-Phong-Song-Sturm and Guedj-T\^o from the case of functions to the framework of twisted differential forms. To this end, we establish certain estimates…

We investigate the action of the automorphism group of an acylindrically hyperbolic group G on its space of homogeneous quasimorphisms, and identify its kernel with the subgroup of "strongly commensurating" automorphisms. We deduce that if…

We revisit Fourier's approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat…

We study semigroup C*-algebras of $ax+b$-semigroups over integral domains. The goal is to generalize several results about C*-algebras of $ax+b$-semigroups over rings of algebraic integers. We prove results concerning K-theory and…

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the…

Let $G$ be a connected, real, semisimple Lie group with finite center, and $K$ a maximal compact subgroup of $G$. In this paper, we derive $K$-equivariant asymptotics for heat traces with remainder estimates on compact Riemannian manifolds…

We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or…

This paper introduces heat semigroups of topological Markov chains and Cuntz-Krieger algebras by means of spectral noncommutative geometry. Using recent advances on the logarithmic Dirichlet Laplacian on Ahlfors regular metric-measure…

We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…

We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff \'{e}tale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse…

Let $A$ be an $n$-dimensional algebra over a field $k$ and $a(A)$ its quantum symmetry semigroup. We prove that the automorphisms group ${\rm Aut}_{\rm Alg} (A)$ of $A$ is isomorphic to the group $U \bigl( G(a (A)^{\rm o} ) \bigl)$ of all…