Related papers: Generators of Noncommutative Dynamics

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…

In 1998, Georgia Benkart and Tom Roby introduced the down-up algebra $\mathcal A$. The algebra $\mathcal A$ is associative, noncommutative, and infinite-dimensional. It is defined by two generators $A,B$ and two relations called the down-up…

We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

Let ${\Bbb F}_{n}$ be the free group of rank $n$ and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C$^{*}$-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n}$ $(1\leq n<\infty$). We introduce a new comultiplication…

We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first…

The pro-algebraic fundamental group can be understood as a completion with respect to finite-dimensional non-commutative algebras. We introduce finer invariants by looking at completions with respect to Banach and C*-algebras, from which we…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

We study the existence of minimal dynamical systems, their orbit and minimal orbit-breaking equivalence relations, and their applications to C*-algebras and K-theory. We show that given any finite CW-complex there exists a space with the…

We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence…

We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among such algebras there are precisely five isomorphism classes.…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…

The purpose of this short note is to clarify and present a general version of an interesting observation by Piani and Mora (Physic. Rev. A 75, 012305 (2007)), linking complete positivity of linear maps on matrix algebras to decomposability…

It is proved that for every $r,s \in \mathbb{N}\backslash \{0,1\}$ the action of $\mathbb{F}_{r+s}$ on $\partial_\beta (\mathbb{F}_{r+s}/\mathbb{F}_r)$ is topologically amenable. In particular the $C^*$-algebra associated to the…

Examples of (strongly continuous) one-parameter groups of automorphisms of UHF C*-algebras are given. One example has the property that the infinitesimal generator does not have a union of finite-dimensional subalgebras as a core. (This…

We show that induction of covariant representations for C*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of…

Almkvist proved that for a commutative ring A the characteristic polynomial of an endomorphism \alpha:P \to P of a finitely generated projective A-module determines (P,\alpha) up to extensions. For a non-commutative ring A the generalized…

We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…

Let X be an infinite compact metric space, \alpha : X \to X a minimal homeomorphism, u the unitary implementing \alpha in the transformation group C*-algebra, and S a class of separable nuclear C*-algebras that contains all unital…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…