Resources for Learning about Graph Algebras

Graph C*-algebras

• Graph Algebras: Bridging the gap between algebra and analysis. (Chapters 1 and 2.) This book is the result of the Workshop on Graph Algebras held July 3--July 8, 2006 in Málaga, Spain that was hosted by the Departmento de Álgebra, Geometrí, y Topología of the Universidad de Málaga. The talks at the meeting were delivered by five speakers, each of whom wrote up the material from their series of talks in a chapter of the book.
• Graph algebras, by Iain Raeburn, CBMS Regional Conference Series in Mathematics, 103. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2005. vi+113 pp.
• The C*-algebras of row-finite graphs, by Teresa Bates, David Pask, Iain Raeburn, and Wojciech Szymański, New York J. Math. 6 (2000), 307--324.
• The ideal structure of the C*-algebras of infinite graphs, by T. Bates, J.H. Hong, I. Raeburn, and W. Szymanski, Illinois J. Math. 46 (2002), no. 4, 1159--1176.
• Resources for learning more about general C*-algebras and K-theory for C*-algebras.
  • C*-algebras and Operator Theory, by Gerard J. Murphy, Academic Press, Inc., Boston, MA, 1990. x+286 pp.
  • C*-algebras by Example, by Kenneth R. Davidson, Fields Institute Monographs, 6. American Mathematical Society, Providence, RI, 1996. xiv+309
  • Morita Equivalence and Continuous-Trace C*-algebras by Iain Raeburn and Dana P. Williams, Mathematical Surveys and Monographs, 60. American Mathematical Society, Providence, RI, 1998. xiv+327 pp.
  • Operator algebras. Theory of C*-algebras and von Neumann algebras, by Bruce Blackadar, Encyclopaedia of Mathematical Sciences, 122. Operator Algebras and Non-commutative Geometry, III. Springer-Verlag, Berlin, 2006. xx+517 pp.
  • An introduction to K-theory for C*-algebras by Mikael Rørdam, Flemming Larsen, and Niels Laustsen, London Mathematical Society Student Texts, 49. Cambridge University Press, Cambridge, 2000. xii+242 pp.
  • K-theory and C*-algebras. A Friendly Approach by N.E. Wegge-Olsen, Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. xii+370 pp.

Leavitt Path Algebras

• Graph Algebras: Bridging the gap between algebra and analysis. (Chapters 3, 4, and 5.)
• Purely infinite simple Leavitt path algebras, by Gene Abrams and Gonzalo Aranda Pino, J. Pure Appl. Algebra 207 (2006), no. 3, 553--563.
• The Leavitt path algebra of a graph, by Gene Abrams and Gonzalo Aranda Pino, J. Algebra 293 (2005), no. 2, 319--334.
• Leavitt path algebras with coefficients in a commutative ring, by Mark Tomforde, J. Pure Appl. Algebra 215 (2011), 471--484.
• Resources for learning more about noncommutative ring theory and algebraic K-theory
  • A First Course in Noncommutative Rings by T.Y. Lam, Second edition. Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 2001. xx+385 pp.
  • Algebra I: Rings, Modules and Categories, by Carl Faith, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 190. Springer-Verlag, Berlin-New York, 1981. xxv+571 pp.
  • Algebra II: Ring Theory, by Carl Faith, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 191. Springer-Verlag, Berlin-New York, 1976. xviii+302 pp.
  • The K-Book: An Introduction to Algebraic K-Theory, by Charles A. Weibel, Graduate Studies in Mathematics, 145. American Mathematical Society, Providence, RI, 2013. 642 pp. (A version of this book is available online for free.)
  • An Algebraic Introduction to K-theory, by Bruce Magurn, Encyclopedia of Mathematics and its Applications, 87. Cambridge University Press, Cambridge, 2002. xiv+676 pp.
  • Algebraic K-Theory and Its Applications, by Jonathan Rosenberg, Graduate Texts in Mathematics, 147. Springer-Verlag, New York, 1994. x+392 pp.

Symbolic Dynamics and Shift Spaces

• An Introduction to Symbolic Dynamics and Coding, by Douglas Lind and Brian Marcus, Cambridge University Press, Cambridge, 1995. xvi+495 pp.
• Symbolic Dynamics. One-Sided, Two-Sided and Countable State Markov Shifts, by Bruce P. Kitchens, Universitext. Springer-Verlag, Berlin, 1998. x+252 pp.