LEADER 03765nam 22006495 450 001 9910257380703321 005 20200701131105.0 010 $a1-4471-7344-9 024 7 $a10.1007/978-1-4471-7344-1 035 $a(DE-He213)978-1-4471-7344-1 035 $a(MiAaPQ)EBC5590036 035 $a(PPN)221248676 035 $a(CKB)4340000000223117 035 $a(EXLCZ)994340000000223117 100 $a20171129d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLeavitt Path Algebras /$fby Gene Abrams, Pere Ara, Mercedes Siles Molina 205 $a1st ed. 2017. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2017. 215 $a1 online resource (XIII, 289 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2191 327 $a1 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 -- Index. 330 $aThis book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2191 606 $aAssociative rings 606 $aRings (Algebra) 606 $aK-theory 606 $aOperator theory 606 $aGraph theory 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 615 0$aAssociative rings. 615 0$aRings (Algebra) 615 0$aK-theory. 615 0$aOperator theory. 615 0$aGraph theory. 615 14$aAssociative Rings and Algebras. 615 24$aK-Theory. 615 24$aOperator Theory. 615 24$aGraph Theory. 676 $a512.74 700 $aAbrams$b Gene$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755746 702 $aAra$b Pere$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSiles Molina$b Mercedes$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910257380703321 996 $aLeavitt Path Algebras$91964433 997 $aUNINA