Triangular Algebras And Ideals Of Nest Algebras

Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 48,7 Mb
Release : 1995-09-28
Category : Mathematics
ISBN : 0821862855

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

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 : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 45,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

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
Page : 436 pages
File Size : 45,6 Mb
Release : 1988
Category : C*-algebras
ISBN : UCAL:B4405476

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Nest Algebras by Kenneth R. Davidson Pdf

Author : Baruch Solel
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 54,8 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821822906

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Irreducible Triangular Algebras by Baruch Solel Pdf

Author : Anonim
Publisher : Unknown
Page : 1596 pages
File Size : 52,7 Mb
Release : 2003
Category : Mathematics
ISBN : UVA:X006180631

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Mathematical Reviews by Anonim Pdf

Author : Edward Cline,Brian Parshall,Leonard Scott,Leonard L. Scott
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 46,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804889

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Stratifying Endomorphism Algebras by Edward Cline,Brian Parshall,Leonard Scott,Leonard L. Scott Pdf

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.

Author : Liangqing Li
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 49,9 Mb
Release : 1997
Category : C*-algebras
ISBN : 9780821805961

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Classification of Simple $C$*-algebras: Inductive Limits of Matrix Algebras over Trees by Liangqing Li Pdf

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.

Author : Dieter Happel,Idun Reiten,Sverre O. Smalø
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 40,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804445

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Tilting in Abelian Categories and Quasitilted Algebras by Dieter Happel,Idun Reiten,Sverre O. Smalø Pdf

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.

Author : Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 52,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805947

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Extended Affine Lie Algebras and Their Root Systems by Bruce Normansell Allison,Saeid Azam,Stephen Berman,Arturo Pianzola,Yun Gao Pdf

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.

Author : H. Andréka,Steven R. Givant,I. Németi
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 54,8 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805954

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Decision Problems for Equational Theories of Relation Algebras by H. Andréka,Steven R. Givant,I. Németi Pdf

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.

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 40,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804032

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Classification of Direct Limits of Even Cuntz-Circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy.

Author : Freddy Dumortier,Robert H. Roussarie
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 55,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804438

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Canard Cycles and Center Manifolds by Freddy Dumortier,Robert H. Roussarie Pdf

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.

Author : Grahame Bennett
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 45,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804360

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Factorizing the Classical Inequalities by Grahame Bennett Pdf

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.

Author : Liviu I. Nicolaescu
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 40,7 Mb
Release : 1997
Category : Geometry, Differential
ISBN : 9780821806210

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Generalized Symplectic Geometries and the Index of Families of Elliptic Problems by Liviu I. Nicolaescu Pdf

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.

Author : Christina Q. He,Michel Laurent Lapidus
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 49,5 Mb
Release : 1997
Category : Differential equations, Partial
ISBN : 9780821805978

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Generalized Minkowski Content, Spectrum of Fractal Drums, Fractal Strings and the Riemann Zeta-Functions by Christina Q. He,Michel Laurent Lapidus Pdf

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.