Lectures on algebraic categorification:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
[2012]
|
| Series: | The QGM master class series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 119 Seiten Diagramme |
| ISBN: | 9783037191088 |
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MARC
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| 100 | 1 | |a Mazorčuk, Volodymyr S. |d 1972- |e Verfasser |0 (DE-588)115278974 |4 aut | |
| 245 | 1 | 0 | |a Lectures on algebraic categorification |c Volodymyr Mazorchuk |
| 264 | 1 | |a Zürich |b European Mathematical Society |c [2012] | |
| 264 | 4 | |c © 2012 | |
| 300 | |a IX, 119 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The QGM master class series | |
| 650 | 0 | 7 | |a Kategorientheorie |0 (DE-588)4120552-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1810687494035865600 |
|---|---|
| adam_text |
Contents
Preface
Basics:
decategorìfìcation
and categorification
1
1.1
The idea of categorification
. 1
1.2
Grothendieck group
. 2
1.3
Decategorification
. 4
1.4
(Pre)categorification of an F-module
. 4
1.5
Graded setup
. 5
1.6
Some constructions
. 6
Basics: from categorification of linear maps to 2-categories
9
2.1
Categorification of linear maps
. 9
2.2
Naïve
categoriHcation
. 9
2.3
Weak categorification
. 11
2.4
2-categories
. 12
2.5
(Genuine) categorification
. 14
Basics: Z-representations of finitary Z-categories
17
3.1
2-representations of 2-categories
. 17
3.2
Fiat-categories
. 18
3.3
Principal 2-representations of fiat-categories
. 19
3.4
Cells
. 20
3.5
Cells modules
. 20
3.6
Homomorphisms from a ceil module
. 22
3.7
Serre subcategories
and quotients
. 22
3.8
Naturally commuting functors
. 22
Category
θ
:
definitions
25
4.1
Definition of category
Θ
. 25
4.2
Verma modules
. 26
4.3
Block decomposition
. 27
4.4
BGG reciprocity and quasi-hereditary structure
. 28
4.5
Tilting modules and
Ringel
self-duality
. 29
4.6
Parabolic category
О
. 30
4.7
g^-example
. ЗІ
viii. Contents
5
Category
Θ:
projective and shuffling functors
33
5.1
Projective functors
. 33
5.2
Translations through walls
. 34
5.3
Description via Harish-Chan
dra
bimodules
. 35
5.4
Shuffling functors
. 36
5.5
Singular braid monoid
. 38
5.6
glj-example
. 39
6
Category
Θ:
twisting and completion
41
6.1
Zuckerman functors
. 41
6.2
Twisting functors
. 41
6.3
Completion functors
. 44
6.4
Alternative description via
(co)
approximations
. 45
6.5
Serre
functor
. 46
7
Category
Θ:
grading and combinatorics
47
7.1
Double centralizer property
. 47
7.2
Hndomorphisms of the
antidominant
projective
. 48
7.3
Grading on
Βχ
. 48
7.4 Hecke
algebra
. 50
7.5
Categorification of the right regular
И
-module
. 51
7.6
Combinatorics of
Θ χ
. 52
8
S
n-categorification: Soergel bimodules, cells and
Specht
modules
55
8.1
Soergei bimodules
. 55
8.2
Kazhdan-Lusztig cells
. 56
8.3
Cell modules
. 57
8.4
Categorification of the induced sign module
. 58
8.5
Categorification of
Specht
modules
. 59
9
%n-categorification: (induced) cell modules
61
9.1
Categories
0^ . 61
9.2
Categorification of cell modules
. 61
9.3
Categorification of permutation modules
. 62
9.4
Parabolic analogues of
С
. 64
9.5
Categorification of induced cell modules
. 65
10
Category©:
Koszul
duality
67
10.1
Quadratic dual of a positively graded algebra
. 67
10.2
Linear complexes of projectives
. 68
10.3
Koszul
duality
. 70
10.4
Koszul
dual functors
. 72
10.5
Alternative categorification of the permutation module
. 72
Contents
ix
11
sli-categorification:
simple fini
te-dimensional
modules
75
11.1
The
algebra Uv(sí2) .
75
11.2
Finite dimensional representations of Uv
(ѕГг).
76
11.3
Catégorisation
of
Vf"
. 77
11.4
Categorification of
V„.
79
11.5
Koszul
dual picture
. 80
12
Application: categorification of the Jones polynomial
81
12.1
Kauffman bracket and Jones polynomial
. 81
12.2
Khovanov's idea for categorification of
J (Ľ).
82
12.3
Quantum sl^-lmk invariants
. 82
12.4
Funcional
quantum
ѕГг-Ипк
invariants
. 84
13
©I
2
-categorification of Chuang and Rouquier
87
13.1
Genuine
5Í2
-categorification
. 87
13.2
Affine
Hecke
algebras
. 88
13.3
Morphisms of sl^-categonfications
. 89
13.4
Minimaisr2-categorificaLi0nofsimplefimte-dimensi0.nalmoduJ.es
. . 90
13.5
sť^-categorification
on category
О
. 91
13.6
Categorification of the simple reflection
. 92
14
Application: blocks of
FfS„]
and
Broué's
conjecture
93
14.1
Jucys-Murphy elements and forma] characters
. 93
14.2
Induction and restriction
. 94
14.3
Categorification of the basic representation of an
affine
Кас
-Moody
algebra
. 95
14.4
Broué's
conjecture
. 95
14.5
Broué's
conjecture for Sn
. 96
14.6
Divided powers
. 97
15
Applications of Srt-categorifications
99
15.1
WedderburnbasisforCfS^]
. 99
15 2
Kostanť s
problem
. 100
15.3
Structure of induced modules
. 102
16
Exercises
105
Bibliography
109
Index
117 |
| any_adam_object | 1 |
| author | Mazorčuk, Volodymyr S. 1972- |
| author_GND | (DE-588)115278974 |
| author_facet | Mazorčuk, Volodymyr S. 1972- |
| author_role | aut |
| author_sort | Mazorčuk, Volodymyr S. 1972- |
| author_variant | v s m vs vsm |
| building | Verbundindex |
| bvnumber | BV040541534 |
| classification_rvk | SK 320 |
| ctrlnum | (OCoLC)782068528 (DE-599)BSZ36233336X |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040541534 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-20T04:22:37Z |
| institution | BVB |
| isbn | 9783037191088 |
| language | English |
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| owner_facet | DE-83 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | IX, 119 Seiten Diagramme |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | European Mathematical Society |
| record_format | marc |
| series2 | The QGM master class series |
| spelling | Mazorčuk, Volodymyr S. 1972- Verfasser (DE-588)115278974 aut Lectures on algebraic categorification Volodymyr Mazorchuk Zürich European Mathematical Society [2012] © 2012 IX, 119 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier The QGM master class series Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Funktor (DE-588)4130706-9 gnd rswk-swf Kategorientheorie (DE-588)4120552-2 s Funktor (DE-588)4130706-9 s Algebra (DE-588)4001156-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-03719-608-3 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025387424&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazorčuk, Volodymyr S. 1972- Lectures on algebraic categorification Kategorientheorie (DE-588)4120552-2 gnd Algebra (DE-588)4001156-2 gnd Funktor (DE-588)4130706-9 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4001156-2 (DE-588)4130706-9 |
| title | Lectures on algebraic categorification |
| title_auth | Lectures on algebraic categorification |
| title_exact_search | Lectures on algebraic categorification |
| title_full | Lectures on algebraic categorification Volodymyr Mazorchuk |
| title_fullStr | Lectures on algebraic categorification Volodymyr Mazorchuk |
| title_full_unstemmed | Lectures on algebraic categorification Volodymyr Mazorchuk |
| title_short | Lectures on algebraic categorification |
| title_sort | lectures on algebraic categorification |
| topic | Kategorientheorie (DE-588)4120552-2 gnd Algebra (DE-588)4001156-2 gnd Funktor (DE-588)4130706-9 gnd |
| topic_facet | Kategorientheorie Algebra Funktor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025387424&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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