Leavitt Path Algebras and Classical K-Theory

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A. A. Ambily, Roozbeh Hazrat, B. Sury
Springer Nature, Jan 17, 2020 - Mathematics - 335 pages

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.

 

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Contents

Part I Leavitt Path Algebras
2
1 A Survey of Some of the Recent Developments in Leavitt Path Algebras
3
2 The Groupoid Approach to Leavitt Path Algebras
21
3 ╔tale Groupoids and Steinberg Algebras a Concise Introduction
73
4 The Injective and Projective Leavitt Complexes
102
5 A Survey on the Ideal Structure of Leavitt Path Algebras
121
6 Gr÷bner Bases and Dimension Formulas for Ternary Partially Associative Operads
139
7 A Survey on Koszul Algebras and Koszul Duality
156
10 A Survey on the Noninjectivity of the Vaserstein Symbol in Dimension Three
192
11 Two Approaches to the BassSuslin Conjecture
203
12 The Pillars of Relative QuillenSuslin Theory
211
13 The Quotient Unimodular Vector Group is Nilpotent
224
14 On a Theorem of Suslin
241
15 On an Algebraic Analogue of the MayerVietoris Sequence
261
16 On the Completability of Unimodular Rows of Length Three
281
17 On a Group Structure on Unimodular Rows of Length Three over a TwoDimensional Ring
307

Part II Classical KTheory
177
8 Symplectic Linearization of an Alternating Polynomial Matrix
179
9 Actions on Alternating Matrices and Compound Matrices
183
18 Relating the Principles of QuillenSuslin Theory
330
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About the author (2020)

A. A. Ambily is Assistant Professor at the Department of Mathematics, Cochin University of Science and Technology, Kerala, India. She holds a Ph.D. in Mathematics from the Indian Statistical Institute, Bangalore Center, India. Her research interests include algebraic K-theory and noncommutative algebras such as Leavitt path algebras and related topics.

Roozbeh Hazrat is Professor at the School of Computer, Data and Mathematical Sciences, Western Sydney University, Australia. He obtained his Ph.D. in Mathematics from the University of Bielefeld, Germany, in 2002. His research interests include Leavitt path algebras, algebraic K-theory and noncommutative algebra. He has authored three books, including Mathematica«: A Problem-Centered Approach published by Springer, and contributed over 50 papers in respected journals. In 2015, he was awarded a one-year fellowship for experienced researchers by Germany's Alexander von Humboldt Foundation.

B. Sury is Professor at the Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Center, India. He received his Ph.D. from the Tata Institute of Fundamental Research, Mumbai, India, in 1991. His research interests include algebraic groups over global and local fields, division algebras, and number theory. He has authored three books and published several research papers in leading international journals. An elected fellow of The National Academy of Sciences, India, Prof. Sury is the national coordinator for the Mathematics Olympiad Program in India.

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