A Friendly Introduction to Path Algebras and Quiver Representations

Abstract

We give an elementary introduction to the theory of quiver representations, which is the foundation of a dynamic area of research. Relying only on basic concepts from linear and abstract algebra, we construct the path algebra of a quiver, and illustrate the notion of the representation type of a finite-dimensional algebra.

MSC::

• Primary 16G20
• Secondary 16G60

ACKNOWLEDGMENTS

This article was written while the author was generously supported by a Manhattan College Summer Grant. The author would like to thank Raymond Maresca, David Pauksztello, Alexander Sistko, and Kathryn Weld for their suggestions, insights, and encouragement. In addition, she is appreciative of the referees’ thoughtful and detailed feedback, which improved the final version.

Additional information

Notes on contributors

Helene R. Tyler

HELENE R. TYLER earned her Ph.D. in mathematics at Syracuse University. Since 2002, she has been a member of the faculty at Manhattan College, where she currently serves as Chair of the Mathematics Department. In addition, she has served several times as a Volunteer Visiting Lecturer at the Royal University of Phnom Penh. She is a past member of the editorial board of the Carus Mathematical Monographs.