Leavitt Path Algebras PDF Download
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Author | : Gene Abrams |
Publisher | : Springer |
Total Pages | : 289 |
Release | : 2017-11-30 |
Genre | : Mathematics |
ISBN | : 1447173449 |
Download Leavitt Path Algebras Book in PDF, ePub and Kindle
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.
Author | : Gene Abrams |
Publisher | : |
Total Pages | : 289 |
Release | : 2017 |
Genre | : Algebra |
ISBN | : 9781447173458 |
Download Leavitt Path Algebras Book in PDF, ePub and Kindle
Author | : Gene Abrams |
Publisher | : Springer |
Total Pages | : 289 |
Release | : 2017-11-30 |
Genre | : Mathematics |
ISBN | : 9781447173434 |
Download Leavitt Path Algebras Book in PDF, ePub and Kindle
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.
Author | : A. A. Ambily |
Publisher | : Springer Nature |
Total Pages | : 340 |
Release | : 2020-01-17 |
Genre | : Mathematics |
ISBN | : 9811516111 |
Download Leavitt Path Algebras and Classical K-Theory Book in PDF, ePub and Kindle
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.
Author | : Pinar Colak |
Publisher | : |
Total Pages | : 0 |
Release | : 2012 |
Genre | : Graph theory |
ISBN | : |
Download Two-sided Ideals in Leavitt Path Algebras Book in PDF, ePub and Kindle
Leavitt path algebras are a natural generalization of the Leavitt algebras, which are a class of algebras introduced by Leavitt in 1962. For a directed graph $E$, the Leavitt path algebra $L_K(E)$ of $E$ with coefficients in $K$ has received much recent attention both from algebraists and analysts over the last decade, due to the fact that they have some immediate structural connections with graph $C*̂$-algebras. So far, some of the algebraic properties of Leavitt path algebras have been investigated, including primitivity, simplicity and being Noetherian. We explicitly describe two-sided ideals in Leavitt path algebras associated to an arbitrary graph. Our main result is that any two-sided ideal $I$ of a Leavitt path algebra associated to an arbitrary directed graph is generated by elements of the form $(v+\sum_{i=1-n} \lambda_i g[superscript i])(v - \sum_{e \in S} ee*̂$), where $g$ is a cycle based at vertex $v$, and $S$ is a finite subset of $s−1(v)$. We first use this result to describe the necessary and sufficient conditions on the arbitrary-sized graph $E$, such that the Leavitt path algebra associated to $E$ satisfies two-sided chain conditions. Then we show that this result can be used to unify and simplify many known results for Leavitt path algebras some of which have been proven by using established methodologies from $C*̂$-algebras.
Author | : Iain Raeburn |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821836609 |
Download Graph Algebras Book in PDF, ePub and Kindle
Graph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C*$-algebras. The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
Author | : Dinh Van Huynh |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2014-02-21 |
Genre | : Mathematics |
ISBN | : 0821887971 |
Download Ring Theory and Its Applications Book in PDF, ePub and Kindle
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.
Author | : Frederick M. Goodman |
Publisher | : Springer Science & Business Media |
Total Pages | : 297 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461396417 |
Download Coxeter Graphs and Towers of Algebras Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : Algebraic fields |
ISBN | : |
Download Units and Leavitt Path Algebras Book in PDF, ePub and Kindle
Author | : Elizabeth Anne Pacheco |
Publisher | : |
Total Pages | : 63 |
Release | : 2019 |
Genre | : Noncommutative algebras |
ISBN | : |
Download New Simple Representations of Leavitt Path Algebras Book in PDF, ePub and Kindle