Related papers: Generators of Detailed Balance Quantum Markov Semi…

We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs samplers beyond finite dimensions raises fundamental obstacles,…

Cipriani and Sauvageot have shown that for any $L^2$-generator $L^{(2)}$ of a tracially symmetric quantum Markov semigroup on a C*-algebra $\mathcal{A}$ there exists a densely defined derivation $\delta$ from $\mathcal{A}$ to a Hilbert…

We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on…

Let $L$ be a non-negative self adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type. Assume that $L$ generates a holomorphic semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy generalized $m$-th order Gaussian…

We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint…

We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf…

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…

For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is…

We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…

It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…

The problem of specification of self-adjoint operators corresponding to singular bilinear forms is very important for applications, such as quantum field theory and theory of partial differential equations with coefficient functions being…

We consider a class of quantum dissipative semigroup on a von-Neumann algebra which admits a normal invariant state. We investigate asymptotic behavior of the dissipative dynamics and their relation to that of the canonical Markov shift. In…

Let $U_q(\hat{\cal G})$ be a quantized affine Lie algebra. It is proven that the universal R-matrix $R$ of $U_q(\hat{\cal G})$ satisfies the celebrated conjugation relation $R^\dagger=TR$ with $T$ the usual twist map. As applications, braid…

Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation.…

In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applications of our construction including the…

A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…

In this paper, we study Markov dynamics on unitary duals of compact quantum groups. We construct such dynamics from characters of quantum groups. Then we show that the dynamics have generators, and we give an explicit formula of the…

We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…

We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…

For a regular representation $H \subseteq \text{Sym}_n$ of the generalized quaternion group of order $n=4k$, with $k\geq 2$, the monoid $S_n(H)$ presented with generators $a_1,a_2,\dots ,a_n$ and with relations $a_1a_2\cdots…