Hilbert space representations of some quantum algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Leipzig, Univ., Diss., 2002 |
| Physical Description: | 103 S. 30 cm |
Staff View
MARC
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Record in the Search Index
| _version_ | 1812460536256790528 |
|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION
5
2 PRELIMINARIES H
2.1 ALGEBRAIC PRELIMINARIES. H
2.2 OPERATOR THEORETIC PRELIMINARIES. 13
3 NON-COMPACT COMODULE ALGEBRAS AND ASSOCIATED CLASSES OF FUNCTIONS 17
3.1 MOTIVATION. 17
3.2 QUANTUM DISC. 18
3.2.1 INVARIANT INTEGRATION ON THE QUANTUM DISC. 18
3.2.2 TOPOLOGICAL ASPECTS OF ^-REPRESENTATIONS. 22
3.2.3 APPLICATION: DIFFERENTIAL CALCULUS . 27
3.3 QUANTUM (N, 1)-MATRIX BALL. 28
3.3.1 INVARIANT INTEGRATION ON THE QUANTUM (N, L)-MATRIX BALL. 28
3.3.2 REPRESENTATIONS OF THE *-ALGEBRA 0(MATG(N. 1)). 34
3.4 REAL QUANTUM HYPERBOLOID. 42
3.5 REAL G-WEYL ALGEBRA. 46
4 CROSS PRODUCT ALGEBRAS 53
4.1 BASICS. ^3
4.2 CROSS PRODUCT ALGEBRAS DF THE HOPF ALGEBRAS
UQ(GH)
AND WG(SI2). 56
4.2.1 DEFINITIONS AND *-STRUCTURES OF
UQIGH), MQ{SH), 0(MQ(
2)) AND
0{SLQ{
2)). 56
4.2.2 CROSS PRODUCT ALGEBRAS OF
UQ(GK)
AND
0(MQ(2))
. 57
4.2.3 THE CROSS PRODUCT *-ALGEBRAWG
(GK)
K
0(C%)
. 58
4.2.4 TWO CROSS PRODUCT *-ALGEBRAS CONTAINING
0(SUQ(2))
. 59
4.2.5 THE CROSS PRODUCT *-ALGEBRA/G(
7
/
2
) * 60
4.2.6 TWO CROSS PRODUCT *-ALGEBRAS CONTAINING
UQ{SUITI)
. 61
4.3 A FIRST APPROACH TO *-REPRESENTATIONS OF CROSS PRODUCT ALGEBRAS. 62
4.3.1 REPRESENTATIONS OF THE COORDINATE *-ALGEBRAS. 63
4.3.2 REPRESENTATIONS OF THE *-ALGEBRA
U0
K
0(SUQ(2))
. 64
4.3.3 REPRESENTATIONS OF THE *-ALGEBRA
UQ(SU
2
)
IX
0(SUQ(
2)). 68
4.3.4 REPRESENTATIONS OF THE *-ALGEBRA . 72
4.3.5 REPRESENTATIONS OF THE *-ALGEBRAL/
9
(GL2)
K 0(R}) . 73
4.3.6 REPRESENTATIONS OF THE *-ALGEBRA
UQ
(SIT(L,L)) IX
0(SUQ(L,L))
. 75
4.3.7 REPRESENTATIONS OF THE *-ALGEBRA
0{UQ)
X
UQ{SU{
1,1)). 78
4.4 HEISENBERG REPRESENTATIONS - A SECOND APPROACH TO ^REPRESENTATIONS.
80
3
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/964520419
4
CONTENTS
4.4.1 HEISENBERG REPRESENTATIONS OF CROSS PRODUCT ALGEBRAS. 80
4.4.2 A UNIQUENESS THEOREM FOR THE HEISENBERG REPRESENTATIONS OF
UQ(SU2)
X
0(SUQ(2)) MDUQ{SU2)
X
0{SF)
. 82
4.4.3 HEISENBERG REPRESENTATIONS OF
UQ(SU2)
TX
0(SUQ(
2)) AND
UQ(SU2)
X
0(S*)
85
4.5 INVARIANT INTEGRATION ON CROSS PRODUCT ALGEBRAS. 88
4.5.1 INVARIANT INTEGRATION ON OPERATOR ALGEBRAS ASSOCIATED WITH CROSS
PRODUCT
ALGEBRAS. 88
4.5.2 A QUANTUM TRACE FORMULA FOR THE HAAR STATE OF
0(SUQ(2))
. 90
4.5.3 THE HAAR STATE OF
0(SUQ(2)}
AS A PARTIAL QUANTUM TRACE. 91
4.6 APPLICATION: COVARIANT DIFFERENTIAL CALCULUS ON QUANTUM GROUPS. 93 |
| any_adam_object | 1 |
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| id | DE-604.BV014447366 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-09T18:04:21Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009874478 |
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| physical | 103 S. 30 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| record_format | marc |
| spelling | Wagner, Elmar 1970- Verfasser (DE-588)123823854 aut Hilbert space representations of some quantum algebras vorgelegt von Elmar Wagner 2002 103 S. 30 cm txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Diss., 2002 Hochschulschrift gtt Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Quantenraum (DE-588)4563053-7 gnd rswk-swf Weyl-Algebra (DE-588)4373964-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Weyl-Algebra (DE-588)4373964-7 s Darstellung Mathematik (DE-588)4128289-9 s Hilbert-Raum (DE-588)4159850-7 s Quantenraum (DE-588)4563053-7 s Operatoralgebra (DE-588)4129366-6 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009874478&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wagner, Elmar 1970- Hilbert space representations of some quantum algebras Hochschulschrift gtt Darstellung Mathematik (DE-588)4128289-9 gnd Operatoralgebra (DE-588)4129366-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Quantenraum (DE-588)4563053-7 gnd Weyl-Algebra (DE-588)4373964-7 gnd |
| subject_GND | (DE-588)4128289-9 (DE-588)4129366-6 (DE-588)4159850-7 (DE-588)4563053-7 (DE-588)4373964-7 (DE-588)4113937-9 |
| title | Hilbert space representations of some quantum algebras |
| title_auth | Hilbert space representations of some quantum algebras |
| title_exact_search | Hilbert space representations of some quantum algebras |
| title_full | Hilbert space representations of some quantum algebras vorgelegt von Elmar Wagner |
| title_fullStr | Hilbert space representations of some quantum algebras vorgelegt von Elmar Wagner |
| title_full_unstemmed | Hilbert space representations of some quantum algebras vorgelegt von Elmar Wagner |
| title_short | Hilbert space representations of some quantum algebras |
| title_sort | hilbert space representations of some quantum algebras |
| topic | Hochschulschrift gtt Darstellung Mathematik (DE-588)4128289-9 gnd Operatoralgebra (DE-588)4129366-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Quantenraum (DE-588)4563053-7 gnd Weyl-Algebra (DE-588)4373964-7 gnd |
| topic_facet | Hochschulschrift Darstellung Mathematik Operatoralgebra Hilbert-Raum Quantenraum Weyl-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009874478&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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