Tag: Algebras

Free Download Operator Algebras and Applications by Aristides Katavolos
English | PDF | 1997 | 470 Pages | ISBN : 0792346254 | 38.1 MB
During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas. The present volume presents a survey of some of the latest developments in the field in a form that is detailed enough to be accessible to advanced graduate students as well as researchers in the field.

Free Download Lie Algebras of Bounded Operators by Daniel Beltiţă , Mihai Şabac
English | PDF | 2001 | 226 Pages | ISBN : 3764364041 | 18.8 MB
In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.

Free Download K-Theory for Operator Algebras by Bruce Blackadar
English | PDF | 1986 | 347 Pages | ISBN : 1461395747 | 26.4 MB
K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others’ subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

Free Download Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky , Haisheng Li
English | PDF (True) | 2004 | 330 Pages | ISBN : 0817634088 | 26.8 MB
Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples

Free Download Geometry of State Spaces of Operator Algebras by Erik M. Alfsen , Frederic W. Shultz
English | PDF (True) | 2003 | 470 Pages | ISBN : 0817643192 | 41.9 MB
In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]’ [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), … ), with reference back to [AS] for proofs, so that this book is self-contained.

Free Download Fundamentals of the Theory of Operator Algebras: Special Topics Volume III Elementary Theory-An Exercise Approach by Richard V. Kadison , John R. Ringrose
English | PDF | 1991 | 285 Pages | ISBN : 1461278341 | 28.7 MB
These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 – I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopCEdic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use of the techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.

Free Download Semigroups, Algebras and Operator Theory: ICSAOT 2022, CUSAT, India, March 28-31 by A. A. Ambily, V. B. Kiran Kumar
English | PDF EPUB (True) | 2024 | 274 Pages | ISBN : 9819963486 | 33.6 MB
This book contains chapters on a range of topics in mathematics and mathematical physics, including semigroups, algebras, operator theory and quantum mechanics, most of them have been presented at the International Conference on Semigroup, Algebras, and Operator Theory (ICSAOT-22), held at Cochin, Kerala, India, from 28-31 March 2022. It highlights the significance of semigroup theory in different areas of mathematics and delves into various themes that demonstrate the subject’s diverse nature and practical applications. One of the key features of the book is its focus on the relationship between geometric algebra and quantum mechanics. The book offers both theoretical and numerical approximation results, presenting a comprehensive overview of the subject. It covers a variety of topics, ranging from C∗-algebraic models to numerical solutions for partial differential equations.

Free Download From Rings and Modules to Hopf Algebras: One Flew over the Algebraist’s Nest
English | 2024 | ISBN: 303150061X | 528 Pages | PDF (True) | 9 MB
Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory ― whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld-Lusztig double of a group algebra, appearing for the first time in a textbook at this level.

Free Download C*-algebras and Elliptic Theory II by Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky
English | PDF (True) | 2008 | 312 Pages | ISBN : 3764386037 | 2.7 MB
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

Free Download Steven Givant, Paul Halmos, "Introduction to Boolean Algebras"
English | 2008 | ISBN: 0387402934, 1441923241 | PDF | pages: 586 | 2.3 mb
This book is an informal yet systematic presentation of lectures given by the author on Boolean algebras. The author’s style is characteristically bold and fresh. He treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled through the text for course study. The second edition has been greatly expanded and rewritten, specific changes include: