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Triangular Algebras And Ideals Of Nest Algebras
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Book Synopsis Triangular Algebras and Ideals of Nest Algebras by : John Lindsay Orr
Download or read book Triangular Algebras and Ideals of Nest Algebras written by John Lindsay Orr and published by American Mathematical Soc.. This book was released on 1995-09-28 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.
Book Synopsis Triangular Algebras and Ideals of Nest Algebras by : John Lindsay Orr
Download or read book Triangular Algebras and Ideals of Nest Algebras written by John Lindsay Orr and published by American Mathematical Soc.. This book was released on 1995 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.
Author :Kenneth R. Davidson Publisher :Harlow, Essex, England : Longman Scientific & Technical ; New York : Wiley ISBN 13 : Total Pages :436 pages Book Rating :4.:/5 (44 download)
Book Synopsis Nest Algebras by : Kenneth R. Davidson
Download or read book Nest Algebras written by Kenneth R. Davidson and published by Harlow, Essex, England : Longman Scientific & Technical ; New York : Wiley. This book was released on 1988 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stratifying Endomorphism Algebras by : Edward Cline
Download or read book Stratifying Endomorphism Algebras written by Edward Cline and published by American Mathematical Soc.. This book was released on 1996 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \mathrm{ End}_R(T)$ be the endomorphism algebra of $T$. This memoir presents a systematic study of the relationships between the representation theories of $R$ and $A$, especially those involving actual or potential structures on $A$ which ''stratify'' its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups. The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ''Specht/Weyl module'' correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.
Book Synopsis Irreducible Triangular Algebras by : Baruch Solel
Download or read book Irreducible Triangular Algebras written by Baruch Solel and published by American Mathematical Soc.. This book was released on 1984 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees by : Liangqing Li
Download or read book Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees written by Liangqing Li and published by American Mathematical Soc.. This book was released on 1997 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, it is shown that the simple unital C*-algebras arising as inductive limits of sequences of finite direct sums of matrix algebras over [italic capital]C([italic capital]X[subscript italic]i), where [italic capital]X[subscript italic]i are arbitrary variable trees, are classified by K-theoretical and tracial data. This result generalizes the result of George Elliott of the case of [italic capital]X[subscript italic]i = [0, 1]. The added generality is useful in the classification of more general inductive limit C*-algebras.
Book Synopsis Tilting in Abelian Categories and Quasitilted Algebras by : Dieter Happel
Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.
Book Synopsis Extended Affine Lie Algebras and Their Root Systems by : Bruce Normansell Allison
Download or read book Extended Affine Lie Algebras and Their Root Systems written by Bruce Normansell Allison and published by American Mathematical Soc.. This book was released on 1997 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is about extended affine Lie algebras (EALA's) and their root systems. EALA's were introduced by Hoegh-Krohn and Torresani under the name irreducible quasi-simple Lie algebras. The major objective is to develop enough theory to provide a firm foundation for further study of EALA's. The first chapter of the paper is devoted to establishing some basic structure theory. It includes a proof of the fact that, as conjectured by Kac, the invariant symmetric bilinear form on an EALA can be scaled so that its restriction to the real span of the root system is positive semi-definite. The second chapter studies extended affine root systems (EARS) which are an axiomatized version of the root systems arising from EALA's. The concept of a semilattice is used to give a complete description of EARS. In the final chapter, a number of new examples of extended affine Lie algebras are given. The concluding appendix contains an axiomatic characterization of the nonisotropic roots in an EARS in a more general context than the one used in the rest of the paper. Features: Provides a foundation for the study of an important class of Lie algebras that generalizes the class of affine Kac-Moody Lie algebras Includes material on Lie algebras and on root systems that can be read independently.
Book Synopsis Decision Problems for Equational Theories of Relation Algebras by : H. Andréka
Download or read book Decision Problems for Equational Theories of Relation Algebras written by H. Andréka and published by American Mathematical Soc.. This book was released on 1997 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a systematic study of decision problems for equational theories of algebras of binary relations (relation algebras). For example, an easily applicable but deep method, based on von Neumann's coordinatization theorem, is developed for establishing undecidability results. The method is used to solve several outstanding problems posed by Tarski. In addition, the complexity of intervals of equational theories of relation algebras with respect to questions of decidability is investigated. Using ideas that go back to Jonsson and Lyndon, the authors show that such intervals can have the same complexity as the lattice of subsets of the set of the natural numbers. Finally, some new and quite interesting examples of decidable equational theories are given. The methods developed in the monograph show promise of broad applicability. They provide researchers in algebra and logic with a new arsenal of techniques for resolving decision questions in various domains of algebraic logic.
Book Synopsis Classification of Direct Limits of Even Cuntz-Circle Algebras by : Huaxin Lin
Download or read book Classification of Direct Limits of Even Cuntz-Circle Algebras written by Huaxin Lin and published by American Mathematical Soc.. This book was released on 1995 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: does not need NBB copy.
Book Synopsis Canard Cycles and Center Manifolds by : Freddy Dumortier
Download or read book Canard Cycles and Center Manifolds written by Freddy Dumortier and published by American Mathematical Soc.. This book was released on 1996 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the ``canard phenomenon'' occurring in Van der Pol's equation $\epsilon \ddot x+(x^2+x)\dot x+x-a=0$ is studied. For sufficiently small $\epsilon >0$ and for decreasing $a$, the limit cycle created in a Hopf bifurcation at $a = 0$ stays of ``small size'' for a while before it very rapidly changes to ``big size'', representing the typical relaxation oscillation. The authors give a geometric explanation and proof of this phenomenon using foliations by center manifolds and blow-up of unfoldings as essential techniques. The method is general enough to be useful in the study of other singular perturbation problems.
Book Synopsis Factorizing the Classical Inequalities by : Grahame Bennett
Download or read book Factorizing the Classical Inequalities written by Grahame Bennett and published by American Mathematical Soc.. This book was released on 1996 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes a new way of looking at the classical inequalities. The most famous such results (Hilbert, Hardy, and Copson) may be interpreted as inclusion relationships, $l^p\subseteq Y$, between certain (Banach) sequence spaces, the norm of the injection being the best constant of the particular inequality. The authors' approach is to replace $l^p$ by a larger space, $X$, with the properties: $\Vert l^p\subseteq X\Vert =1$ and $\Vert X\subseteq Y\Vert =\Vert l^p\subseteq Y\Vert$, the norm on $X$ being so designed that the former property is intuitive. Any such result constitutes an enhancement of the original inequality, because you now have the classical estimate, $\Vert l^p\subseteq Y\Vert$, holding for a larger collection, $X=Y$. The authors' analysis has some noteworthy features: The inequalities of Hilbert, Hardy, and Copson (and others) all share the same space $Y$. That space-alias ces($p$ )-being central to so many celebrated inequalities, the authors conclude, must surely be important. It is studied here in considerable detail. The renorming of $Y$ is based upon a simple factorization, $Y= l^p\cdot Z$ (coordinatewise products), wherein $Z$ is described explicitly. That there is indeed a renorming, however, is not so simple. It is proved only after much preparation when duality theory is considered.
Book Synopsis Generalized Symplectic Geometries and the Index of Families of Elliptic Problems by : Liviu I. Nicolaescu
Download or read book Generalized Symplectic Geometries and the Index of Families of Elliptic Problems written by Liviu I. Nicolaescu and published by American Mathematical Soc.. This book was released on 1997 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an index theorem is proved for arbitrary families of elliptic boundary value problems for Dirac operators and a surgery formula for the index of a family of Dirac operators on a closed manifold. Also obtained is a very general result on the cobordism invariance of the index of a family. All results are established by first symplectically rephrasing the problems and then using a generalized symplectic reduction technique. This provides a unified approach to all possible parameter spaces and all possible symmetries of a Dirac operator (eigh symmetries in the real case and two in the complex case). This text will also be of interest to those working in geometry and topology.
Book Synopsis Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions by : Christina Q. He
Download or read book Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions written by Christina Q. He and published by American Mathematical Soc.. This book was released on 1997 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir provides a detailed study of the effect of non power-like irregularities of (the geometry of) the fractal boundary on the spectrum of "fractal drums" (and especially of "fractal strings"). In this work, the authors extend previous results in this area by using the notionof generalized Minkowski content which is defined through some suitable "gauge functions" other than power functions. (This content is used to measure the irregularity (or "fractality") of the boundary of an open set in R]n by evaluating the volume of its small tubular neighborhoods). In the situation when the power function is not the natural "gauge function", this enables the authors to obtain more precise estimates, with a broader potential range of applications than in previous papers of the second author and his collaborators. This text will also be of interest to those working in mathematical physics.
Book Synopsis Operators of Class C_0 with Spectra in Multiply Connected Regions by : Adele Zucchi
Download or read book Operators of Class C_0 with Spectra in Multiply Connected Regions written by Adele Zucchi and published by American Mathematical Soc.. This book was released on 1997 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\Omega$ be a bounded finitely connected region in the complex plane, whose boundary $\Gamma$ consists of disjoint, analytic, simple closed curves. The author considers linear bounded operators on a Hilbert space $H$ having $\overline \Omega$ as spectral set, and no normal summand with spectrum in $\gamma$. For each operator satisfying these properties, the author defines a weak$^*$-continuous functional calculus representation on the Banach algebra of bounded analytic functions on $\Omega$. An operator is said to be of class $C_0$ if the associated functional calculus has a non-trivial kernel. In this work, the author studies operators of class $C_0$, providing a complete classification into quasisimilarity classes, which is analogous to the case of the unit disk.
Book Synopsis Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations by : Moshé Flato
Download or read book Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations written by Moshé Flato and published by American Mathematical Soc.. This book was released on 1997 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this work is to present and give full proofs of new original research results concerning integration of and scattering for the classical Maxwell-Dirac equations. These equations govern first quantized electrodynamics and are the starting point for a rigorous formulation of quantum electrodynamics. The presentation is given within the formalism of nonlinear group and Lie algebra representations, i.e. the powerful new approach to nonlinear evolution equations covariant under a group action. The authors prove that the nonlinear Lie algebra representation given by the manifestly covariant Maxwell-Dirac equations is integrable to a global nonlinear representation of the Poincare group on a differentiable manifold of small initial conditions. This solves, in particular, the small-data Cauchy problem for the Maxwell-Dirac equations globally in time. The existence of modified wave operators and asymptotic completeness is proved. The asymptotic representations (at infinite time) turn out to be nonlinear. A cohomological interpretation of the results in the spirit of nonlinear representation theory and its connection to the infrared tail of the electron are developed.
Book Synopsis Axiomatic Stable Homotopy Theory by : Mark Hovey
Download or read book Axiomatic Stable Homotopy Theory written by Mark Hovey and published by American Mathematical Soc.. This book was released on 1997 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a 'stable homotopy category'; using these axioms, one can make various constructions - cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories. Next, a number of examples of such categories are presented. Some of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). Hence one can apply many of the tools of stable homotopy theory to these algebraic situations.This work: provides a reference for standard results and constructions in stable homotopy theory; discusses applications of those results to algebraic settings, such as group theory and commutative algebra; provides a unified treatment of several different situations in stable homotopy, including equivariant stable homotopy and localizations of the stable homotopy category; and, also provides a context for nilpotence and thick subcategory theorems, such as the nilpotence theorem of Devinatz-Hopkins-Smith and the thick subcategory theorem of Hopkins-Smith in stable homotopy theory, and the thick subcategory theorem of Benson-Carlson-Rickard in representation theory. This book presents stable homotopy theory as a branch of mathematics in its own right with applications in other fields of mathematics. It is a first step toward making stable homotopy theory a tool useful in many disciplines of mathematics.
