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Titel:	Leavitt path algebras
Von:	Gene Abrams, Pere Ara, Mercedes Siles Molina
Person:	Abrams, Gene aut Ara, Pere Siles Molina, Mercedes 1959-
Hauptverfassende:	Abrams, Gene (VerfasserIn), Ara, Pere 1959- (VerfasserIn), Siles Molina, Mercedes (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	London Springer [2017]
Schriftenreihe:	Lecture notes in mathematics 2191
Notation:	SI 850
Schlagwörter:	K-Theorie Graphentheorie Assoziativer Ring PBV Leavitt path algebras ideal structure Leavitt path algebras structure of idempotents K-theory algebraic K-theory Leavitt path algebras applications Leavitt path algebras generalizations
Medienzugang:	http://deposit.dnb.de/cgi-bin/dokserv?id=1b437bd8c7c649aeac6abb5586b06c97&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030098509&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xiii, 287 Seiten
ISBN:	9781447173434 1447173430

Internformat

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Datensatz im Suchindex

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adam_text	Gene Abrams • Pere Ara • Mercedes Siles Molina Leavitt Path Algebras Springer Contents 1 The Basics of Leavitt Path Algebras: Motivations, Definitions and Examples 1 11A Motivating Construction: The Leavitt Algebras 2 1 2 Leavitt Path Algebras 5 1 3 The Three Fundamental Examples of Leavitt Path Algebras 10 1 4 Connections and Motivations: The Algebras of Bergman, and Graph C-Algebras 12 1 5 The Cohn Path Algebras and Connections to Leavitt Path Algebras 14 1 6 Direct Limits in the Context of Leavitt Path Algebras 23 17A Brief Retrospective on the History of Leavitt Path Algebras 30 2 Two-Sided Ideals 33 2 1 TheZ-Grading 36 2 2 The Reduction Theorem and the Uniqueness Theorems 46 2 3 Additional Consequences of the Reduction Theorem 54 2 4 Graded Ideals: Basic Properties and Quotient Graphs 56 2 5 The Structure Theorem for Graded Ideals, and the Internal Structure of Graded Ideals 65 2 6 The Socle 76 2 7 The Ideal Generated by the Vertices in Cycles Without Exits 83 2 8 The Structure Theorem for Ideals, and the Internal Structure of Ideals 89 2 9 Additional Consequences of the Structure Theorem for Ideals The Simplicity Theorem 97 3 Idempotents, and Finitely Generated Projective Modules 103 3 1 Purely Infinite Simplicity, and the Dichotomy Principle 104 3 2 Finitely Generated Projective Modules: The iC-Monoid 108 3 3 The Exchange Property 116 3 4 Von Neumann Regularity 121 3 5 Primitive Non-Minimal Idempotents 125 xi xii Contents 3 6 Structural Properties of the V-Monoid 128 3 7 Extreme Cycles 137 3 8 Purely Infinite Without Simplicity 140 4 General Ring-Theoretic Results 151 4 1 Prime and Primitive Ideals in Leavitt Path Algebras of Row-Finite Graphs 151 4 2 Chain Conditions on One-Sided Ideals 158 4 3 Self-Injectivity 167 4 4 The Stable Rank 173 5 Graph C -Algebras, and Their Relationship to Leavitt Path Algebras 185 51A Brief Overview of C-Algebras 185 5 2 Graph C-Algebras, and Connections to Leavitt Path Algebras 190 5 3 Projections in Graph C-Algebras 198 5 4 Closed Ideals of Graph C-Algebras Containing No Vertices 204 5 5 The Structure of Closed Ideals of Graph C-Algebras of Row-Finite Graphs 209 5 6 Comparing Properties of Leavitt Path Algebras and Graph C -Algebras 212 6 K-Theory 219 6 1 The Grothendieck Group Kq{Lk(E)) 219 6 2 The Whitehead Group K {Lk(E)) 225 6 3 The Algebraic Kirchberg-Phillips Question 230 6 4 Tensor Products and Hochschild Homology 248 7 Generalizations, Applications, and Current Lines of Research 259 7 1 Generalizations of Leavitt Path Algebras 259 711 Leavitt Path Algebras of Separated Graphs 260 712 Kumjian-Pask Algebras 261 713 Steinberg Algebras: The Groupoid Approach 261 714 Non-Field Coefficients 263 7 2 Applications of Leavitt Path Algebras 263 721 Isomorphisms Between Matrix Rings over Leavitt Algebras: Applications to Higman-Thompson Groups 263 722 Primitive Leavitt Path Algebras: A Systematic Answer to a Question of Kaplansky 265 723 The Regular Algebra of a Graph: The Realization Problem for von Neumann Regular Rings 267 7 3 Current Lines of Research in Leavitt Path Algebras 267 731 The Classification Question for Purely Infinite Simple Leavitt Path Algebras, aka “The Algebraic Kirchberg-Phillips Question’’ 268 732 Tensor Products 270 Contents xiii 733 The Classification Question for Graphs with Finitely Many Vertices and Infinitely Many Edges 270 734 Graded Grothendieck Groups, and the Corresponding Graded Classification Conjecture 271 735 Connections to Noncommutative Algebraic Geometry 273 References 275
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physical	xiii, 287 Seiten
publishDate	2017
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publishDateSort	2017
publisher	Springer
record_format	marc
series	Lecture notes in mathematics
series2	Lecture notes in mathematics
spellingShingle	Abrams, Gene Ara, Pere 1959- Siles Molina, Mercedes Leavitt path algebras Lecture notes in mathematics K-Theorie (DE-588)4033335-8 gnd Graphentheorie (DE-588)4113782-6 gnd Assoziativer Ring (DE-588)4143228-9 gnd
subject_GND	(DE-588)4033335-8 (DE-588)4113782-6 (DE-588)4143228-9
title	Leavitt path algebras
title_auth	Leavitt path algebras
title_exact_search	Leavitt path algebras
title_full	Leavitt path algebras Gene Abrams, Pere Ara, Mercedes Siles Molina
title_fullStr	Leavitt path algebras Gene Abrams, Pere Ara, Mercedes Siles Molina
title_full_unstemmed	Leavitt path algebras Gene Abrams, Pere Ara, Mercedes Siles Molina
title_short	Leavitt path algebras
title_sort	leavitt path algebras
topic	K-Theorie (DE-588)4033335-8 gnd Graphentheorie (DE-588)4113782-6 gnd Assoziativer Ring (DE-588)4143228-9 gnd
topic_facet	K-Theorie Graphentheorie Assoziativer Ring
url	http://deposit.dnb.de/cgi-bin/dokserv?id=1b437bd8c7c649aeac6abb5586b06c97&prov=M&dok_var=1&dok_ext=htm http://www.springer.com/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030098509&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT abramsgene leavittpathalgebras AT arapere leavittpathalgebras AT silesmolinamercedes leavittpathalgebras AT springerverlaglondonltd leavittpathalgebras

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