02384nam a2200397 i 4500991003614329707536190227s2017 nyu 000 0 eng d9781447173434(alk. paper)1447173430b14360317-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng512.223AMS 16-02Leavitt path algebras /[edited by] Gene Abrams, Pere Ara, Mercedes Siles MolinaNew York, NY :Springer,2017xiii, 289 p. ;ill. ;24 cmtexttxtrdacontentunmediatednrdamediavolumencrdacarrierLecture notes in mathematics,0075-8434 ;21911 The basics of Leavitt path algebras: motivations, definitions and examples ; 2 Two-sided ideals ; 3 Idempotents, and finitely generated projective modules ; 4 General ring-theoretic results , 5 Graph C*-algebras, and their relationship to Leavitt path algebras ; 6 K-theory ; 7 Generalizations, applications, and current lines of research ; References ; IndexThis text offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebrasAssociative ringsRings (Algebra)K-theoryOperator theoryGraph theoryAbrams, GeneAra, PereSiles Molina, Mercedes.b1436031715-03-1927-02-19991003614329707536LE013 16-XX ABR11 (2017)12013000230122le013pE57.19-l- 00000.i1588352815-03-19Leavitt path algebras1749690UNISALENTOle01327-02-19ma -engnyu00