Leavitt path algebras:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
[2017]
|
| Schriftenreihe: | Lecture notes in mathematics
2191 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis |
| Beschreibung: | xiii, 287 Seiten |
| ISBN: | 9781447173434 1447173430 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV044701825 | ||
| 003 | DE-604 | ||
| 005 | 20180417 | ||
| 007 | t | ||
| 008 | 180108s2017 xxk |||| 00||| eng d | ||
| 016 | 7 | |a 1132075386 |2 DE-101 | |
| 020 | |a 9781447173434 |c Book : circa EUR 48.14 (DE) (freier Preis), circa EUR 49.49 (AT) (freier Preis), circa CHF 49.50 (freier Preis) |9 978-1-4471-7343-4 | ||
| 020 | |a 1447173430 |9 1-4471-7343-0 | ||
| 024 | 3 | |a 9781447173434 | |
| 028 | 5 | 2 | |a Bestellnummer: 978-1-4471-7343-4 |
| 028 | 5 | 2 | |a Bestellnummer: 86849719 |
| 035 | |a (OCoLC)1019658904 | ||
| 035 | |a (DE-599)DNB1132075386 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a xxk |c XA-GB | ||
| 049 | |a DE-29T |a DE-355 |a DE-11 |a DE-83 |a DE-824 |a DE-188 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a 16Sxx |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Abrams, Gene |4 aut | |
| 245 | 1 | 0 | |a Leavitt path algebras |c Gene Abrams, Pere Ara, Mercedes Siles Molina |
| 264 | 1 | |a London |b Springer |c [2017] | |
| 264 | 4 | |c © 2017 | |
| 300 | |a xiii, 287 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2191 | |
| 650 | 0 | 7 | |a K-Theorie |0 (DE-588)4033335-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Assoziativer Ring |0 (DE-588)4143228-9 |2 gnd |9 rswk-swf |
| 653 | |a PBV | ||
| 653 | |a Leavitt path algebras | ||
| 653 | |a ideal structure Leavitt path algebras | ||
| 653 | |a structure of idempotents | ||
| 653 | |a K-theory | ||
| 653 | |a algebraic K-theory | ||
| 653 | |a Leavitt path algebras applications | ||
| 653 | |a Leavitt path algebras generalizations | ||
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | 1 | |a K-Theorie |0 (DE-588)4033335-8 |D s |
| 689 | 0 | 2 | |a Assoziativer Ring |0 (DE-588)4143228-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Ara, Pere |d 1959- |0 (DE-588)12401688X |4 aut | |
| 700 | 1 | |a Siles Molina, Mercedes |4 aut | |
| 710 | 2 | |a Springer-Verlag London Ltd. |0 (DE-588)1065358059 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4471-7344-1 |
| 830 | 0 | |a Lecture notes in mathematics |v 2191 |w (DE-604)BV000676446 |9 2191 | |
| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=1b437bd8c7c649aeac6abb5586b06c97&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
| 856 | 4 | 2 | |m X:MVB |u http://www.springer.com/ |
| 856 | 4 | 2 | |m HEBIS Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-030098509 | |
Datensatz im Suchindex
| _version_ | 1806414398430904320 |
|---|---|
| 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 |
| any_adam_object | 1 |
| author | Abrams, Gene Ara, Pere 1959- Siles Molina, Mercedes |
| author_GND | (DE-588)12401688X |
| author_facet | Abrams, Gene Ara, Pere 1959- Siles Molina, Mercedes |
| author_role | aut aut aut |
| author_sort | Abrams, Gene |
| author_variant | g a ga p a pa m m s mm mms |
| building | Verbundindex |
| bvnumber | BV044701825 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)1019658904 (DE-599)DNB1132075386 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV044701825</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20180417</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">180108s2017 xxk |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1132075386</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781447173434</subfield><subfield code="c">Book : circa EUR 48.14 (DE) (freier Preis), circa EUR 49.49 (AT) (freier Preis), circa CHF 49.50 (freier Preis)</subfield><subfield code="9">978-1-4471-7343-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1447173430</subfield><subfield code="9">1-4471-7343-0</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781447173434</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">Bestellnummer: 978-1-4471-7343-4</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">Bestellnummer: 86849719</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1019658904</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1132075386</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxk</subfield><subfield code="c">XA-GB</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16Sxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Abrams, Gene</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Leavitt path algebras</subfield><subfield code="c">Gene Abrams, Pere Ara, Mercedes Siles Molina</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Springer</subfield><subfield code="c">[2017]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2017</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiii, 287 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2191</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">K-Theorie</subfield><subfield code="0">(DE-588)4033335-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Assoziativer Ring</subfield><subfield code="0">(DE-588)4143228-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">PBV</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Leavitt path algebras</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">ideal structure Leavitt path algebras</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">structure of idempotents</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">K-theory</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">algebraic K-theory</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Leavitt path algebras applications</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Leavitt path algebras generalizations</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">K-Theorie</subfield><subfield code="0">(DE-588)4033335-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Assoziativer Ring</subfield><subfield code="0">(DE-588)4143228-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ara, Pere</subfield><subfield code="d">1959-</subfield><subfield code="0">(DE-588)12401688X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Siles Molina, Mercedes</subfield><subfield code="4">aut</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Springer-Verlag London Ltd.</subfield><subfield code="0">(DE-588)1065358059</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4471-7344-1</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2191</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2191</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="q">text/html</subfield><subfield code="u">http://deposit.dnb.de/cgi-bin/dokserv?id=1b437bd8c7c649aeac6abb5586b06c97&prov=M&dok_var=1&dok_ext=htm</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">X:MVB</subfield><subfield code="u">http://www.springer.com/</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HEBIS Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030098509</subfield></datafield></record></collection> |
| id | DE-604.BV044701825 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-04T00:23:36Z |
| institution | BVB |
| institution_GND | (DE-588)1065358059 |
| isbn | 9781447173434 1447173430 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030098509 |
| oclc_num | 1019658904 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR DE-11 DE-83 DE-824 DE-188 |
| owner_facet | DE-29T DE-355 DE-BY-UBR DE-11 DE-83 DE-824 DE-188 |
| physical | xiii, 287 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Abrams, Gene aut Leavitt path algebras Gene Abrams, Pere Ara, Mercedes Siles Molina London Springer [2017] © 2017 xiii, 287 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2191 K-Theorie (DE-588)4033335-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Assoziativer Ring (DE-588)4143228-9 gnd rswk-swf 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 Graphentheorie (DE-588)4113782-6 s K-Theorie (DE-588)4033335-8 s Assoziativer Ring (DE-588)4143228-9 s 1\p DE-604 Ara, Pere 1959- (DE-588)12401688X aut Siles Molina, Mercedes aut Springer-Verlag London Ltd. (DE-588)1065358059 pbl Erscheint auch als Online-Ausgabe 978-1-4471-7344-1 Lecture notes in mathematics 2191 (DE-604)BV000676446 2191 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=1b437bd8c7c649aeac6abb5586b06c97&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ HEBIS Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |