Tomforde, Mark2019-09-132019-09-13May 20192019-05May 2019https://hdl.handle.net/10657/4457Directed graphs have played a prominent role as a tool for encoding information for certain classes of C*-algebras, particularly AF-algebras and Cuntz-Krieger algebras. These constructions have been generalized to a class of C*-algebras known as graph C*-algebras, which have found applications to several areas of C*-algebra theory. One prominent area of investigation has been the application of Elliott’s classification program to the class of graph C*-algebras. Rørdam was able to prove that K-theory invariants classify certain simple Cuntz-Krieger algebras, and this classification has been extended to broader classes of graph C*-algebras, including even certain non-simple cases. Another avenue for extending these classification results is to consider Leavitt path algebras, algebraic analogues of the graph C*-algebras, and ask to what extent K-theory groups can be used to classify them. This dissertation explores a specific, but important, aspect of the classification of Leavitt path algebras. In particular, we investigate the question of whether L(E2) and L(E2−) are *-isomorphic. We do this by examining the diagonal of a Leavitt path algebra, and producing methods to construct endomorphisms of Leavitt path algebras that take a given maximal abelian subalgebra (MASA) to the diagonal.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Leavitt path algebraEndomorphisms2019-09-13Thesisborn digital