On K-theory of Leavitt path algebras

Abstract

In 1960's, W. G. Leavitt introduced a type of non-commutative algebras that are now called Leavitt Algebras. In 2005, Gene Abrams and Gonzalo Aranda Pino introduced Leavitt path algebras as a generalization of Leavitt algebras. It was also done by Pere Ara, María Moreno, and Enrique Pardo simultaneously. In this thesis we explain K_0 and K_1 groups of Leavitt path algebras, based on the studies of Gene Abrams, Pere Ara and Mercedes Siles Molina.