Representations of infinite dimensional groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
American Math. Soc.
1996
|
| Series: | Translations of mathematical monographs
152 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 197 S. |
| ISBN: | 0821804189 |
Staff View
MARC
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| 240 | 1 | 0 | |a Predstavlenija beskonečnomernych grupp |
| 245 | 1 | 0 | |a Representations of infinite dimensional groups |c R. S. Ismagilov |
| 246 | 1 | 3 | |a Representations of infinite-dimensional groups |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1996 | |
| 300 | |a X, 197 S. | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 152 | |
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| 650 | 4 | |a Loops (Group theory) | |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 1. Some General Constructions Related to Representations 5
§1. Preliminary results (groups representations and cohomology, mea¬
surable spaces, dynamical systems) 5
§2. Some generalizations of induced representations. Generalized de¬
terminant bundle and an extension of the group GL° 9
§3. The space S(H) (bosonic Fock space) and a representation of the
group H ¦ Sp(H) 18
§4. Representations of the Lie algebra H+sp(H); representations of
the canonical commutation relations (CCR) 27
§5. The space A(H) (the fermionic Fock space) and a representation
of the group O(H) 29
§6. Representations of groups in the space S(H); the Araki scheme 32
§7. Irreducibility and equivalence of representations Tb r 33
§8. Another irreducibility criterion for the representations Tu r 35
Chapter 2. Representations of the Group of Measurable Currents 41
§9. Factorizable operators in the Fock space S(H), H = L2{X, n, H°);
the convexity theorem 41
§10. Representations of the group Gx (the Araki construction) 55
§11. Examples 58
§12. Continuous tensor products (CTP) of Hilbert spaces and represen¬
tation of the group Gx 60
§13. The group Tx ¦ M(X, fj) 65
Chapter 3. Representations of the Group of Smooth Currents 67
§14. Energy representations of the group C^{X, G) 67
§15. Properties of Gaussian measures related to Dirichlet forms 69
§16. Irreducibility and pairwise nonequivalence of energy representa¬
tions of the group Cq°(X, G) 81
§17. Projective unitary representations of the group Co°(X,G); repre¬
sentations of the universal covering group 83
§18. Certain group extensions associated to dynamical systems and to
canonical commutation relations (CCR); extensions of the current
groups 87
§19. Representations of Mickelsson Rajeev extensions 90
ix
x CONTENTS
Chapter 4. Certain Results on Diffeomorphism Groups 93
§20. Diffeomorphism groups 93
§21. The group D(X) theorem on adjoint elements 95
§22. Groups of volume preserving diffeomorphisms 99
§23. Groups of volume preserving diffeomorphisms (continuation); em¬
bedding into a semidirect product 102
§24. Groups of symplectomorphisms 105
§25. An example of an infinite dimensional symplectic manifold 112
§26. The action of diffeomorphism groups on the configuration spaces
flm(I); small subgroups 118
Chapter 5. Representations of Diffeomorphism Groups Associated with Con¬
figuration Spaces 123
§27. Class O representations of the group D(X); the commutative op¬
erator algebra generated by a representation 123
§28. Description of class O representations ([15]) 125
§29. On dynamical systems of the form (fi,/x, D(X)); the Shavgulidze
measure 131
§30. Representations associated to spaces of finite configurations 131
§31. Representations of the group DiS1) associated to countable con¬
figurations with one limit point ([14]) 141
§32. Representations of the group D(Rn) associated to the Poisson mea¬
sure 146
Chapter 6. Representations of Certain Group Extensions 153
§33. Representations of the group Tx ¦ M(X, /x) 153
§34. Representations of the group CDO(Rn,E) D(Kn); Goldin Grodnik
Powers Sharp uniqueness theorem 158
Chapter 7. Representations of Diffeomorphism Groups in the Fock Space 167
§35. Description of representations; formulation of the problem 167
§36. Representations of the groups D(X, vn) and D(X, vn) in the Fock
space 168
§37. Representations of the group D0(X,lj2) in the Fock space 173
§38. Concluding remarks about the representations of diffeomorphism
groups 178
Chapter 8. Representations of Groups of Foliation Preserving Diffeomor¬
phisms 179
§39. Brief description of the results 179
§40. Groups and homogeneous domains associated to type II factors 180
§41. The group D(T2,6 ), its embedding into Sp°M, and its projective
representations 185
§42. The Lie algebra V^(T2,6), its embedding into sp°M, and projective
representations 191
§43. Concluding remarks 194
References 195
|
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| dewey-full | 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.55 |
| dewey-search | 512/.55 |
| dewey-sort | 3512 255 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010992358 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:02:15Z |
| institution | BVB |
| isbn | 0821804189 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007357412 |
| oclc_num | 34544575 |
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| owner_facet | DE-12 DE-29T DE-11 DE-188 |
| physical | X, 197 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Ismagilov, Rais S. Verfasser aut Predstavlenija beskonečnomernych grupp Representations of infinite dimensional groups R. S. Ismagilov Representations of infinite-dimensional groups Providence, RI American Math. Soc. 1996 X, 197 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 152 Aus dem Russ. übers. Lacets (Théorie des groupes) ram Lie, groupes de ram Représentations de groupes ram Lie groups Loops (Group theory) Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Translations of mathematical monographs 152 (DE-604)BV000002394 152 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007357412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ismagilov, Rais S. Representations of infinite dimensional groups Translations of mathematical monographs Lacets (Théorie des groupes) ram Lie, groupes de ram Représentations de groupes ram Lie groups Loops (Group theory) Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4130355-6 |
| title | Representations of infinite dimensional groups |
| title_alt | Predstavlenija beskonečnomernych grupp Representations of infinite-dimensional groups |
| title_auth | Representations of infinite dimensional groups |
| title_exact_search | Representations of infinite dimensional groups |
| title_full | Representations of infinite dimensional groups R. S. Ismagilov |
| title_fullStr | Representations of infinite dimensional groups R. S. Ismagilov |
| title_full_unstemmed | Representations of infinite dimensional groups R. S. Ismagilov |
| title_short | Representations of infinite dimensional groups |
| title_sort | representations of infinite dimensional groups |
| topic | Lacets (Théorie des groupes) ram Lie, groupes de ram Représentations de groupes ram Lie groups Loops (Group theory) Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Lacets (Théorie des groupes) Lie, groupes de Représentations de groupes Lie groups Loops (Group theory) Representations of groups Darstellungstheorie Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007357412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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