Noncommutative Dynamics and E-Semigroups
Noncommutative Dynamics and E-Semigroups

Author: William Arveson

Publisher: Springer Science & Business Media

Published: 2012-11-06

Total Pages: 442

ISBN-13: 0387215247

DOWNLOAD EBOOK

This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

Advances in Quantum Dynamics
Advances in Quantum Dynamics

Author: Geoffrey L. Price

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 338

ISBN-13: 0821832158

DOWNLOAD EBOOK

This volume contains the proceedings of the conference on Advances in Quantum Dynamics. The purpose of the conference was to assess the current state of knowledge and to outline future research directions of quantum dynamical semigroups on von Neumann algebras. Since the appearance of the landmark papers by F. Murray and J. von Neumann, On the Rings of Operators, von Neumann algebras have been used as a mathematical model in the study of time evolution of quantum mechanical systems.Following the work of M. H. Stone, von Neumann, and others on the structure of one-parameter groups of unitary transformations, many researchers have made fundamental contributions to the understanding of time-reversible dynamical systems. This book deals with the mathematics of time-irreversiblesystems, also called dissipative systems. The time parameter is the half-line, and the transformations are now endomorphisms as opposed to automorphisms. For over a decade, W. B. Arveson and R. T. Powers have pioneered the effort to understand the structure of irreversible quantum dynamical systems on von Neumann algebras. Their papers in this volume serve as an excellent introduction to the theory. Also included are contributions in other areas which have had an impact on the theory, such asBrownian motion, dilation theory, quantum probability, and free probability. The volume is suitable for graduate students and research mathematicians interested in the dynamics of quantum systems and corresponding topics in the theory of operator algebras.

The Spectrum of a Module Category
The Spectrum of a Module Category

Author: Henning Krause

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 143

ISBN-13: 0821826182

DOWNLOAD EBOOK

These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.

Equivariant $E$-Theory for $C^*$-Algebras
Equivariant $E$-Theory for $C^*$-Algebras

Author: Erik Guentner

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 101

ISBN-13: 0821821164

DOWNLOAD EBOOK

This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space

Non-Additive Exact Functors and Tensor Induction for Mackey Functors
Non-Additive Exact Functors and Tensor Induction for Mackey Functors

Author: Serge Bouc

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 89

ISBN-13: 0821819518

DOWNLOAD EBOOK

First the author introduces a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category. Next those results are used to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for p-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.

Cocycles of CCR Flows
Cocycles of CCR Flows

Author: B. V. Rajarama Bhat

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 130

ISBN-13: 0821826328

DOWNLOAD EBOOK

We study the partially ordered set of quantum dynamical semigroups dominated by a given semigroup on the algebra of all bounded operators on a Hilbert space. For semigroups of *-endomorphisms this set can be described through cocycles. This helps us to prove a factorization theorem for dilations and to show that minimal dilations of quantum dynamical semigroups with bounded generators can be got through Hudson-Parthasarathy cocycles.