{"id":{"repo_id":"houston","oai_identifier":"oai:uh-ir.tdl.org:10657/4457"},"canonical_url":"https://search.dev.ndltd.org/etd/houston/oai:uh-ir.tdl.org:10657/4457","repository":{"repo_id":"houston","name":"University of Houston","base_url":"https://uh-ir.tdl.org/server/oai/request"},"display":{"title":"Endomorphisms of Leavitt Path Algebras","abstract":"Directed 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.","abstract_html":"Directed 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.","abstract_has_math":false,"creators":["Haque, Mozahid"],"institution":"University of Houston","degree_name":"Doctor of Philosophy","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Tomforde, Mark"],"committee_chairs":[],"committee_members":["Kalantar, Mehrdad","Ott, William","Cheng, Albert M. K."],"year":2019,"date_issued":"2019-05","date_published":"2019-05","updated_at":"2026-07-24T02:33:06Z","subjects":["Leavitt path algebra","Endomorphisms"],"languages":["eng"],"rights":["The 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)."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10657/4457","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Tomforde, Mark"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kalantar, Mehrdad","Ott, William","Cheng, Albert M. 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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)."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10657/4457"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Directed 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."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Endomorphisms of Leavitt Path Algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Tomforde, Mark"],"dc:contributor.committeemember":["Kalantar, Mehrdad","Ott, William","Cheng, Albert M. K."],"dc:creator":["Haque, Mozahid"],"dc:date.accessioned":["2019-09-13T01:09:25Z"],"dc:date.available":["2019-09-13T01:09:25Z"],"dc:date.issued":["2019-05"],"dc:description.abstract":["Directed 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."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10657/4457"],"dc:language.iso":["eng"],"dc:rights":["The 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)."],"dc:subject":["Leavitt path algebra","Endomorphisms"],"dc:title":["Endomorphisms of Leavitt Path Algebras"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["University of Houston"]},"updated_at":"2026-07-24T02:33:06Z"}