Lie semigroups and their applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1552 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 315 S. graph. Darst. |
| ISBN: | 3540569545 0387569545 |
Internformat
MARC
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| 100 | 1 | |a Hilgert, Joachim |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lie semigroups and their applications |c Joachim Hilgert ; Karl-Hermann Neeb |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a XII, 315 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1552 | |
| 650 | 7 | |a Cône convexe fermé |2 Jussieu | |
| 650 | 4 | |a Lie, Groupes de | |
| 650 | 7 | |a Lie, Groupes de |2 ram | |
| 650 | 7 | |a Lie-groepen |2 gtt | |
| 650 | 7 | |a Représentation semi-groupe |2 Jussieu | |
| 650 | 7 | |a Semi-groupe Olshanskij |2 Jussieu | |
| 650 | 4 | |a Semi-groupes | |
| 650 | 7 | |a Semigroepen |2 gtt | |
| 650 | 7 | |a Semigroupe Lie |2 Jussieu | |
| 650 | 7 | |a Semigroupes |2 ram | |
| 650 | 7 | |a Théorème Lüscher-Mack |2 Jussieu | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Semigroups | |
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| 700 | 1 | |a Neeb, Karl-Hermann |d 1964- |e Verfasser |0 (DE-588)112163920 |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 1552 |w (DE-604)BV000676446 |9 1552 | |
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Datensatz im Suchindex
| _version_ | 1805082756805296128 |
|---|---|
| adam_text |
Table of Contents
1. Lie semigroups and their tangent wedges
1.1 Geometry of wedges 1
1.2 Wedges in A' modules 9
1.3 The characteristic function of a cone 11
Endomorphisms of a cone 18
1.4 Lie wedges and Lie semigroups 19
The ordered space of Lorentzian cones 21
Affine compressions of a ball 23
1.5 Functorial relations between Lie semigroups and Lie wedges 25
1.6 Globality of Lie wedges 28
1.7 Monotone functions and semigroups 29
1.8 Smooth and analytic monotone functions on a Lie group 32
1.9 PK positive functions and globality 38
1.10 Globality criteria 42
2. Examples
2.1 Semigroups in the Heisenberg group 48
2.2 The groups Sl(2) and PS1(2, IR) 49
2.3 The hyperboloid and its order structure 56
2.4 The Olshanski! semigroup in S1(2,C) 59
2.5 Affine compression semigroups 61
2.6 The euclidean compression and contraction semigroups 63
2.7 Godel's cosmological model and the universal covering of Sl(2, IR) 65
2.8 The causal action of SU(n,n) on U(n) 68
The action of SU(n, n) on the euclidean contraction semigroup 69
2.9 Almost abelian groups 73
2.10 The whirlpot and the parking ramp 73
2.11 The oscillator group 76
vi
3. Geometry and topology of Lie semigroups
3.1 Faces of Lie semigroups 81
3.2 The interior of Lie semigroups 86
3.3 Non generating Lie semigroups with interior points 88
3.4 The universal covering semigroup 5 90
3.5 The free group on 5 101
3.6 Groups with directed orders 107
4. Ordered homogeneous spaces
4.1 Chains in metric pospaces 114
4.2 Invariant cone fields on homogeneous spaces 121
4.3 Globality of cone fields 126
4.4 Chains and conal curves 130
4.5 Covering spaces and globality 135
4.6 Regular ordered homogeneous spaces 138
4.7 Extremal curves 140
5. Applications of ordered spaces to Lie semigroups
5.1 Consequences of the Globality Theorem 148
5.2 Consequences of the Covering Theorem 149
5.3 Conal curves and reachability in semigroups 153
5.4 Applications to faces of Lie semigroups 156
5.5 Monotone curves in Lie semigroups 159
6. Maximal semigroups in groups with cocompact radical
6.1 Hyperplane subalgebras of Lie algebras 162
6.2 Elementary facts about maximal semigroups 164
6.3 Abelian and almost abelian groups 166
6.4 Nilpotent groups 167
6.5 Reduction lemmas 169
6.6 Characterization of maximal subsemigroups 171
6.7 Applications to reachability questions 173
vii
7. Invariant Cones and Ol'shanskiT semigroups
7.1 Compactly embedded Cartan algebras 177
7.2 Invariant cones in Lie algebras 184
7.3 Lawson's Theorem on OlshanskiT semigroups 194
Symmetric Lie algebras 194
Ol'shanskii wedges 195
8. Compression semigroups
8.1 Invariant control sets 203
8.2 Moment maps and projective spaces 209
8.3 Pseudo unitary representations and orbits on flag manifolds 218
Complex semisimple Lie algebras 218
Highest weight modules 219
Real forms and open orbits 221
Wolf's analysis of open orbits in complex flag manifolds 223
Pseudo unitary representations 226
Pseudo unitarizability of representations 227
Moment mappings 229
Pseudo Kahler structures on open G orbits 230
8.4 Compression semigroups of open G orbits 232
8.5 Contraction semigroups for indefinite forms 246
The complex case 247
The real case 249
8.6 Maximality of complex Ol'shanskii semigroups 250
9. Representation theory
9.1 Involutive semigroups 254
9.2 Holomorphic representations of half planes 257
9.3 Invariant cones and unitary representations 262
Some properties of holomorphic contraction representations 268
9.4 Holomorphic discrete series representations 269
9.5 Hardy spaces 276
Cauchy Szego kernels 282
Examples: Cones in euclidean space 286
Examples: The polydisc 287
Examples: The holomorphic discrete series 287
viii
9.6 Howe's oscillator semigroup 288
9.7 The Luscher Mack Theorem 291
10. The theory for Sl(2)
Lie wedges and globality 297
Global hyperbolicity 298
Maximal semigroups with interior points 298
The holomorphic discrete series for SU(1,1) 298
References 303
List of Symbols 311
Index 313 |
| any_adam_object | 1 |
| author | Hilgert, Joachim Neeb, Karl-Hermann 1964- |
| author_GND | (DE-588)112163920 |
| author_facet | Hilgert, Joachim Neeb, Karl-Hermann 1964- |
| author_role | aut aut |
| author_sort | Hilgert, Joachim |
| author_variant | j h jh k h n khn |
| building | Verbundindex |
| bvnumber | BV008097437 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 206f MAT 225f |
| ctrlnum | (OCoLC)246273854 (DE-599)BVBBV008097437 |
| dewey-full | 510 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.55 |
| dewey-search | 510 512/.55 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008097437 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:37:43Z |
| institution | BVB |
| isbn | 3540569545 0387569545 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005334839 |
| oclc_num | 246273854 |
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| physical | XII, 315 S. graph. Darst. |
| publishDate | 1993 |
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| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Hilgert, Joachim Verfasser aut Lie semigroups and their applications Joachim Hilgert ; Karl-Hermann Neeb Berlin [u.a.] Springer 1993 XII, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1552 Cône convexe fermé Jussieu Lie, Groupes de Lie, Groupes de ram Lie-groepen gtt Représentation semi-groupe Jussieu Semi-groupe Olshanskij Jussieu Semi-groupes Semigroepen gtt Semigroupe Lie Jussieu Semigroupes ram Théorème Lüscher-Mack Jussieu Lie groups Semigroups Lie-Halbgruppe (DE-588)4329948-9 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s DE-604 Lie-Halbgruppe (DE-588)4329948-9 s Neeb, Karl-Hermann 1964- Verfasser (DE-588)112163920 aut Lecture notes in mathematics 1552 (DE-604)BV000676446 1552 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005334839&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hilgert, Joachim Neeb, Karl-Hermann 1964- Lie semigroups and their applications Lecture notes in mathematics Cône convexe fermé Jussieu Lie, Groupes de Lie, Groupes de ram Lie-groepen gtt Représentation semi-groupe Jussieu Semi-groupe Olshanskij Jussieu Semi-groupes Semigroepen gtt Semigroupe Lie Jussieu Semigroupes ram Théorème Lüscher-Mack Jussieu Lie groups Semigroups Lie-Halbgruppe (DE-588)4329948-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4329948-9 (DE-588)4130355-6 |
| title | Lie semigroups and their applications |
| title_auth | Lie semigroups and their applications |
| title_exact_search | Lie semigroups and their applications |
| title_full | Lie semigroups and their applications Joachim Hilgert ; Karl-Hermann Neeb |
| title_fullStr | Lie semigroups and their applications Joachim Hilgert ; Karl-Hermann Neeb |
| title_full_unstemmed | Lie semigroups and their applications Joachim Hilgert ; Karl-Hermann Neeb |
| title_short | Lie semigroups and their applications |
| title_sort | lie semigroups and their applications |
| topic | Cône convexe fermé Jussieu Lie, Groupes de Lie, Groupes de ram Lie-groepen gtt Représentation semi-groupe Jussieu Semi-groupe Olshanskij Jussieu Semi-groupes Semigroepen gtt Semigroupe Lie Jussieu Semigroupes ram Théorème Lüscher-Mack Jussieu Lie groups Semigroups Lie-Halbgruppe (DE-588)4329948-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Cône convexe fermé Lie, Groupes de Lie-groepen Représentation semi-groupe Semi-groupe Olshanskij Semi-groupes Semigroepen Semigroupe Lie Semigroupes Théorème Lüscher-Mack Lie groups Semigroups Lie-Halbgruppe Lie-Algebra |
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| volume_link | (DE-604)BV000676446 |
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