Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 0821815458
Total Pages : 135 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras by : Joachim Zacharias

Download or read book Continuous Tensor Products and Arveson's Spectral $C^*$-Algebras written by Joachim Zacharias and published by American Mathematical Soc.. This book was released on 2000 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in operator algebras

Noncommutative Dynamics and E-Semigroups

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Publisher : Springer Science & Business Media
ISBN 13 : 0387215247
Total Pages : 442 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Noncommutative Dynamics and E-Semigroups by : William Arveson

Download or read book Noncommutative Dynamics and E-Semigroups written by William Arveson and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : American Mathematical Soc.
ISBN 13 : 0821832158
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advances in Quantum Dynamics by : Geoffrey L. Price

Download or read book Advances in Quantum Dynamics written by Geoffrey L. Price and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Splitting Theorems for Certain Equivariant Spectra

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Publisher : American Mathematical Soc.
ISBN 13 : 082182046X
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Splitting Theorems for Certain Equivariant Spectra by : L. Gaunce Lewis

Download or read book Splitting Theorems for Certain Equivariant Spectra written by L. Gaunce Lewis and published by American Mathematical Soc.. This book was released on 2000 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in algebraic topology.

The Spectrum of a Module Category

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826182
Total Pages : 143 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Spectrum of a Module Category by : Henning Krause

Download or read book The Spectrum of a Module Category written by Henning Krause and published by American Mathematical Soc.. This book was released on 2001 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : American Mathematical Soc.
ISBN 13 : 0821821164
Total Pages : 101 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Equivariant $E$-Theory for $C^*$-Algebras by : Erik Guentner

Download or read book Equivariant $E$-Theory for $C^*$-Algebras written by Erik Guentner and published by American Mathematical Soc.. This book was released on 2000 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821821105
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions by : Paul Selick

Download or read book On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions written by Paul Selick and published by American Mathematical Soc.. This book was released on 2000 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in topology and representation theory.

Non-Additive Exact Functors and Tensor Induction for Mackey Functors

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Publisher : American Mathematical Soc.
ISBN 13 : 0821819518
Total Pages : 89 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Non-Additive Exact Functors and Tensor Induction for Mackey Functors by : Serge Bouc

Download or read book Non-Additive Exact Functors and Tensor Induction for Mackey Functors written by Serge Bouc and published by American Mathematical Soc.. This book was released on 2000 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826328
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Cocycles of CCR Flows by : B. V. Rajarama Bhat

Download or read book Cocycles of CCR Flows written by B. V. Rajarama Bhat and published by American Mathematical Soc.. This book was released on 2001 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Black Box Classical Groups

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826190
Total Pages : 183 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Black Box Classical Groups by : William M. Kantor

Download or read book Black Box Classical Groups written by William M. Kantor and published by American Mathematical Soc.. This book was released on 2001 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.

Homogeneous Integral Table Algebras of Degree Three: A Trilogy

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820214
Total Pages : 109 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homogeneous Integral Table Algebras of Degree Three: A Trilogy by : Harvey I. Blau

Download or read book Homogeneous Integral Table Algebras of Degree Three: A Trilogy written by Harvey I. Blau and published by American Mathematical Soc.. This book was released on 2000 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.

Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826697
Total Pages : 79 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra by : William Norrie Everitt

Download or read book Multi-Interval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra written by William Norrie Everitt and published by American Mathematical Soc.. This book was released on 2001 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multi-interval quasi-differential system $\{I_{r},M_{r},w_{r}:r\in\Omega\}$ consists of a collection of real intervals, $\{I_{r}\}$, as indexed by a finite, or possibly infinite index set $\Omega$ (where $\mathrm{card} (\Omega)\geq\aleph_{0}$ is permissible), on which are assigned ordinary or quasi-differential expressions $M_{r}$ generating unbounded operators in the Hilbert function spaces $L_{r}^{2}\equiv L^{2}(I_{r};w_{r})$, where $w_{r}$ are given, non-negative weight functions. For each fixed $r\in\Omega$ assume that $M_{r}$ is Lagrange symmetric (formally self-adjoint) on $I_{r}$ and hence specifies minimal and maximal closed operators $T_{0,r}$ and $T_{1,r}$, respectively, in $L_{r}^{2}$. However the theory does not require that the corresponding deficiency indices $d_{r}^{-}$ and $d_{r}^{+}$ of $T_{0,r}$ are equal (e. g. the symplectic excess $Ex_{r}=d_{r}^{+}-d_{r}^{-}\neq 0$), in which case there will not exist any self-adjoint extensions of $T_{0,r}$ in $L_{r}^{2}$. In this paper a system Hilbert space $\mathbf{H}:=\sum_{r\,\in\,\Omega}\oplus L_{r}^{2}$ is defined (even for non-countable $\Omega$) with corresponding minimal and maximal system operators $\mathbf{T}_{0}$ and $\mathbf{T}_{1}$ in $\mathbf{H}$. Then the system deficiency indices $\mathbf{d}^{\pm} =\sum_{r\,\in\,\Omega}d_{r}^{\pm}$ are equal (system symplectic excess $Ex=0$), if and only if there exist self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$ in $\mathbf{H}$. The existence is shown of a natural bijective correspondence between the set of all such self-adjoint extensions $\mathbf{T}$ of $\mathbf{T}_{0}$, and the set of all complete Lagrangian subspaces $\mathsf{L}$ of the system boundary complex symplectic space $\mathsf{S}=\mathbf{D(T}_{1})/\mathbf{D(T}_{0})$. This result generalizes the earlier symplectic version of the celebrated GKN-Theorem for single interval systems to multi-interval systems. Examples of such complete Lagrangians, for both finite and infinite dimensional complex symplectic $\mathsf{S}$, illuminate new phenoma for the boundary value problems of multi-interval systems. These concepts have applications to many-particle systems of quantum mechanics, and to other physical problems.

Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820486
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension by : Guy David

Download or read book Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension written by Guy David and published by American Mathematical Soc.. This book was released on 2000 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.

Proper Maps of Toposes

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Publisher : American Mathematical Soc.
ISBN 13 : 0821821687
Total Pages : 125 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Proper Maps of Toposes by : Ieke Moerdijk

Download or read book Proper Maps of Toposes written by Ieke Moerdijk and published by American Mathematical Soc.. This book was released on 2000 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop the theory of compactness of maps between toposes, together with associated notions of separatedness. This theory is built around two versions of "propriety" for topos maps, introduced here in a parallel fashion. The first, giving what we simply call "proper" maps, is a relatively weak condition due to Johnstone. The second kind of proper maps, here called "tidy", satisfy a stronger condition due to Tierney and Lindgren. Various forms of the Beck-Chevalley condition for (lax) fibered product squares of toposes play a central role in the development of the theory. Applications include a version of the Reeb stability theorem for toposes, a characterization of hyperconnected Hausdorff toposes as classifying toposes of compact groups, and of strongly Hausdorff coherent toposes as classifiying toposes of profinite groupoids. Our results also enable us to develop further particular aspects of the factorization theory of geometric morphisms studied by Johnstone. Our final application is a (so-called lax) descent theorem for tidy maps between toposes. This theorem implies the lax descent theorem for coherent toposes, conjectured by Makkai and proved earlier by Zawadowski.

Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821827626
Total Pages : 74 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions by : Milé Krajčevski

Download or read book Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions written by Milé Krajčevski and published by American Mathematical Soc.. This book was released on 2001 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in group theory and generalizations.

Blowing Up of Non-Commutative Smooth Surfaces

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Publisher : American Mathematical Soc.
ISBN 13 : 0821827545
Total Pages : 157 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Blowing Up of Non-Commutative Smooth Surfaces by : M. van den Bergh

Download or read book Blowing Up of Non-Commutative Smooth Surfaces written by M. van den Bergh and published by American Mathematical Soc.. This book was released on 2001 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.

Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820680
Total Pages : 143 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras by : Doug Pickrell

Download or read book Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras written by Doug Pickrell and published by American Mathematical Soc.. This book was released on 2000 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.