Leavitt Path Algebras
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Leavitt Path Algebras
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Author : Gene Abrams
language : en
Publisher: Springer
Release Date : 2017-11-30
Leavitt Path Algebras written by Gene Abrams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-30 with Mathematics categories.
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.
Leavitt Path Algebras
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Author : Gene Abrams
language : en
Publisher:
Release Date : 2017
Leavitt Path Algebras written by Gene Abrams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Algebra categories.
Leavitt Path Algebras And Classical K Theory
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Author : A. A. Ambily
language : en
Publisher: Springer Nature
Release Date : 2020-01-17
Leavitt Path Algebras And Classical K Theory written by A. A. Ambily and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-17 with Mathematics categories.
The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.
Leavitt Path Algebras
DOWNLOAD
Author : Gene Abrams
language : en
Publisher: Springer
Release Date : 2017-11-30
Leavitt Path Algebras written by Gene Abrams and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-30 with Mathematics categories.
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.
Ring Theory And Its Applications
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Author : Dinh Van Huynh
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-02-21
Ring Theory And Its Applications written by Dinh Van Huynh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-21 with Mathematics categories.
This volume contains the proceedings of the Ring Theory Session in honor of T. Y. Lam's 70th birthday, at the 31st Ohio State-Denison Mathematics Conference, held from May 25-27, 2012, at The Ohio State University, Columbus, Ohio. Included are expository articles and research papers covering topics such as cyclically presented modules, Eggert's conjecture, the Mittag-Leffler conditions, clean rings, McCoy rings, QF rings, projective and injective modules, Baer modules, and Leavitt path algebras. Graduate students and researchers in many areas of algebra will find this volume valuable as the papers point out many directions for future work; in particular, several articles contain explicit lists of open questions.
Graded Rings And Graded Grothendieck Groups
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Author : Roozbeh Hazrat
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-26
Graded Rings And Graded Grothendieck Groups written by Roozbeh Hazrat and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Mathematics categories.
This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Operator Algebras And Applications
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Author : Toke M. Carlsen
language : en
Publisher: Springer
Release Date : 2016-07-30
Operator Algebras And Applications written by Toke M. Carlsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-30 with Mathematics categories.
Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Coxeter Graphs And Towers Of Algebras
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Author : Frederick M. Goodman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Coxeter Graphs And Towers Of Algebras written by Frederick M. Goodman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the fundamental nature of the new link invariants has led to connections with invariant theory, statistical mechanics and quantum theory. In turn, the link invariants, the notion of a quantum group, and the quantum Yang-Baxter equation have had a great impact on the study of subfactors. Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.
2016 Matrix Annals
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Author : Jan de Gier
language : en
Publisher: Springer
Release Date : 2018-04-10
2016 Matrix Annals written by Jan de Gier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-10 with Mathematics categories.
MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.
Noncommutative Motives
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Author : Gonçalo Tabuada
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-09-21
Noncommutative Motives written by Gonçalo Tabuada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Algebraic varieties categories.
The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.