Galois theories of linear difference equations: an introduction
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2016]
|
| Series: | Mathematical surveys and monographs
volume 211 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 171 Seiten Diagramme |
| ISBN: | 9781470426552 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV043730227 | ||
| 003 | DE-604 | ||
| 005 | 20230824 | ||
| 007 | t | ||
| 008 | 160824s2016 |||| |||| 00||| eng d | ||
| 010 | |a 2015039225 | ||
| 020 | |a 9781470426552 |c Hardcover |9 978-1-4704-2655-2 | ||
| 035 | |a (OCoLC)951144804 | ||
| 035 | |a (DE-599)GBV837547938 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-91G |a DE-11 | ||
| 050 | 0 | |a QA431 | |
| 082 | 0 | |a 515/.625 | |
| 084 | |a SK 200 |0 (DE-625)143223: |2 rvk | ||
| 084 | |a 31.24 |2 bkl | ||
| 084 | |a MAT 126f |2 stub | ||
| 100 | 1 | |a Hardouin, Charlotte |d 1977- |e Verfasser |0 (DE-588)1117943267 |4 aut | |
| 245 | 1 | 0 | |a Galois theories of linear difference equations |b an introduction |c Charlotte Hardouin, Jacques Sauloy, Michael F. Singer |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a x, 171 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v volume 211 | |
| 650 | 4 | |a Difference equations | |
| 650 | 4 | |a Galois theory | |
| 650 | 0 | 7 | |a Galois-Theorie |0 (DE-588)4155901-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Galois-Theorie |0 (DE-588)4155901-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sauloy, Jacques |d 1953- |e Verfasser |0 (DE-588)1048245764 |4 aut | |
| 700 | 1 | |a Singer, Michael F. |d 1950- |e Verfasser |0 (DE-588)115533265 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-2940-9 |
| 830 | 0 | |a Mathematical surveys and monographs |v volume 211 |w (DE-604)BV000018014 |9 211 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029142112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029142112 | ||
Record in the Search Index
| _version_ | 1804176528844521472 |
|---|---|
| adam_text | Titel: Galois theories of linear difference equations
Autor: Hardouin, Charlotte
Jahr: 2016
Contents
Preface ix
Algebraic and Algorithmic Aspects of Linear Difference Equations
by Michael F. Singer 1
1. Introduction 1
2. Algebraic varieties 2
2.1. Varieties and ideals 3
2.2. Irreducible varieties 4
2.3. Morphisms and coordinate rings 6
2.4. Problems 8
3. Linear algebraic groups 8
3.1. Linear algebraic groups 8
3.2. Lie-Kolchin theorem 11
3.3. Torsors 11
3.4. Problems 12
4. Picard-Vessiot extensions 13
4.1. Difference rings and fields 13
4.2. Linear difference equations and Picard-Vessiot extensions 14
4.3. Applications 19
4.4. Problems 20
5. Picard-Vessiot groups 20
5.1. Galois groups of PV extensions 20
5.2. PV extensions and torsors 21
5.3. Applications 23
5.4. Galois correspondence 25
5.5. Problems 27
6. Computational questions 27
6.1. Calculating PV groups and algebraic relations among Solutions
of linear difference equations 27
6.2. Liouvillian sequences 31
7. Hints and answers to problems 36
7.1. Problems for Section 2 36
7.2. Problems for Section 3 37
7.3. Problems for Section 4 38
7.4. Problems for Section 5 39
References 40
V
vi
CONTENTS
Galoisian Approach to Differential Transcendence
by Charlotte Hardouin 43
1. Introduction 43
2. Differential algebraic equations from an algebraic point of view 45
2.1. Differential rings 45
2.2. Differential ideals 48
2.3. Differential polynomial rings and differential algebras 50
2.4. Differential fields 57
3. Differential algebraic geometry 63
3.1. Differential algebraic sets 64
3.2. fc-d-coordinate rings and fc-d-morphisms 66
3.3. Dimension of a /c-d-closed set 70
3.4. From algebraic geometry to differential algebraic geometry
and vice versa 71
3.5. Linear fc- 5-groups 71
4. Parametrized Picard-Vessiot theory 78
4.1. The framework 79
4.2. Parametrized Picard-Vessiot rings 80
4.3. The parametrized Galois group 88
4.4. Applications to differential transcendence and isomonodromic
Problems 92
References 99
Analytic Study of q-Difference Equations
by Jacques Sauloy 103
1. Introduction and motivation: q-analogies 106
1.1. Euler, the master of the series 106
1.2. q-analogues and q-degeneracies 110
1.3. Exercises on Section 1 114
2. Some difference and q-difference algebra 115
2.1. Difference fields 115
2.2. Difference Operators 117
2.3. Difference equations 118
2.4. Difference Systems 120
2.5. Difference modules 122
2.6. Exercises on Section 2 124
3. Fuchsian q-difference equations and Systems 126
3.1. Definitions and criteria 126
3.2. Local reduction and Classification 127
3.3. Solving fuchsian Systems 129
3.4. Local and global Classification of fuchsian Systems 132
3.5. Two examples 134
3.6. Exercises on Section 3 136
4. Galois and q-monodromy groups of fuchsian Systems 139
4.1. Local fuchsian differential Galois group and monodromy group 139
4.2. Local fuchsian q-difference Galois group and q-monodromy group 143
4.3. Global fuchsian q-difference Galois group and q-monodromy group 148
4.4. Exercises on Section 4 149
CONTENTS vii
5. Slopes and filtration 150
5.1. The Newton polygon of an Operator 150
5.2. Factorisation of Operators 151
5.3. The Adams filtration 156
5.4. Birkhoff-Guenther normal form 159
5.5. Growth of Solutions 163
5.6. Exercises on Section 5 164
A. Confluence 164
A.l. What lies behind q-degeneracies 164
A.2. Degeneracy of basic functions when q — 1 165
A.3. Degeneracy of canonical Solutions when q — 1 166
A.4. Degeneracy of Birkhoff s matrix when q — 1 167
A.5. Basic hypergeometric series again 168
A.6. Exercises on Appendix ? 169
References 169
|
| any_adam_object | 1 |
| author | Hardouin, Charlotte 1977- Sauloy, Jacques 1953- Singer, Michael F. 1950- |
| author_GND | (DE-588)1117943267 (DE-588)1048245764 (DE-588)115533265 |
| author_facet | Hardouin, Charlotte 1977- Sauloy, Jacques 1953- Singer, Michael F. 1950- |
| author_role | aut aut aut |
| author_sort | Hardouin, Charlotte 1977- |
| author_variant | c h ch j s js m f s mf mfs |
| building | Verbundindex |
| bvnumber | BV043730227 |
| callnumber-first | Q - Science |
| callnumber-label | QA431 |
| callnumber-raw | QA431 |
| callnumber-search | QA431 |
| callnumber-sort | QA 3431 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 200 |
| classification_tum | MAT 126f |
| ctrlnum | (OCoLC)951144804 (DE-599)GBV837547938 |
| dewey-full | 515/.625 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.625 |
| dewey-search | 515/.625 |
| dewey-sort | 3515 3625 |
| 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>01894nam a2200469 cb4500</leader><controlfield tag="001">BV043730227</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230824 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">160824s2016 |||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2015039225</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781470426552</subfield><subfield code="c">Hardcover</subfield><subfield code="9">978-1-4704-2655-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)951144804</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBV837547938</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="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA431</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.625</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 200</subfield><subfield code="0">(DE-625)143223:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.24</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 126f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hardouin, Charlotte</subfield><subfield code="d">1977-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1117943267</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Galois theories of linear difference equations</subfield><subfield code="b">an introduction</subfield><subfield code="c">Charlotte Hardouin, Jacques Sauloy, Michael F. Singer</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2016]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2016</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">x, 171 Seiten</subfield><subfield code="b">Diagramme</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">Mathematical surveys and monographs</subfield><subfield code="v">volume 211</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Difference equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Galois theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Galois-Theorie</subfield><subfield code="0">(DE-588)4155901-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Galois-Theorie</subfield><subfield code="0">(DE-588)4155901-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sauloy, Jacques</subfield><subfield code="d">1953-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1048245764</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Singer, Michael F.</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)115533265</subfield><subfield code="4">aut</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">978-1-4704-2940-9</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">volume 211</subfield><subfield code="w">(DE-604)BV000018014</subfield><subfield code="9">211</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=029142112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029142112</subfield></datafield></record></collection> |
| id | DE-604.BV043730227 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:37Z |
| institution | BVB |
| isbn | 9781470426552 |
| language | English |
| lccn | 2015039225 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029142112 |
| oclc_num | 951144804 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 |
| physical | x, 171 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Hardouin, Charlotte 1977- Verfasser (DE-588)1117943267 aut Galois theories of linear difference equations an introduction Charlotte Hardouin, Jacques Sauloy, Michael F. Singer Providence, Rhode Island American Mathematical Society [2016] © 2016 x, 171 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs volume 211 Difference equations Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s DE-604 Sauloy, Jacques 1953- Verfasser (DE-588)1048245764 aut Singer, Michael F. 1950- Verfasser (DE-588)115533265 aut Erscheint auch als Online-Ausgabe 978-1-4704-2940-9 Mathematical surveys and monographs volume 211 (DE-604)BV000018014 211 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029142112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hardouin, Charlotte 1977- Sauloy, Jacques 1953- Singer, Michael F. 1950- Galois theories of linear difference equations an introduction Mathematical surveys and monographs Difference equations Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4155901-0 |
| title | Galois theories of linear difference equations an introduction |
| title_auth | Galois theories of linear difference equations an introduction |
| title_exact_search | Galois theories of linear difference equations an introduction |
| title_full | Galois theories of linear difference equations an introduction Charlotte Hardouin, Jacques Sauloy, Michael F. Singer |
| title_fullStr | Galois theories of linear difference equations an introduction Charlotte Hardouin, Jacques Sauloy, Michael F. Singer |
| title_full_unstemmed | Galois theories of linear difference equations an introduction Charlotte Hardouin, Jacques Sauloy, Michael F. Singer |
| title_short | Galois theories of linear difference equations |
| title_sort | galois theories of linear difference equations an introduction |
| title_sub | an introduction |
| topic | Difference equations Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Difference equations Galois theory Galois-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029142112&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT hardouincharlotte galoistheoriesoflineardifferenceequationsanintroduction AT sauloyjacques galoistheoriesoflineardifferenceequationsanintroduction AT singermichaelf galoistheoriesoflineardifferenceequationsanintroduction |