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Hilgert J., Neeb K.-H. — Lie Semigroups and their Applications
Hilgert J., Neeb K.-H. — Lie Semigroups and their Applications

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Название: Lie Semigroups and their Applications

Авторы: Hilgert J., Neeb K.-H.

Аннотация:

Subsemigroups of finite-dimensional Lie groups that are generated by one-parameter semigroups are the subject ofthis book. It covers basic Lie theory for such semigroupsand some closely related topics. These include orderedhomogeneous manifolds, where the order is defined by a fieldof cones, invariant cones in Lie algebras and associatedOl'shanskii semigroups. Applications to representationtheory, symplectic geometry and Hardy spaces are also given.The book is written as an efficient guide for thoseinterested in subsemigroups of Lie groups and theirapplications in various fields of mathematics (see theUser's guide at the end of the Introduction). Since it isessentially self-contained and leads directly to the core ofthe theory, the first part of the book can also serve as anintroduction to the subject.The reader is merely expected to be familiar with the basictheory of Lie groups and Lie algebras.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 315

Добавлена в каталог: 15.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolutely continuous      123
Accessible on      203
Admissible representation      277
Almost abelian group      73
Analytic mapping      257
Antichain condition      134
Backward set      114
Bargmann — Fock Hilbert space      288
Base ideal      163
Base root      163
Basic system      87
Basis of a positive system of roots      219
Bergman-type condition      279
Borel subalgebra      218
Borel subgroup      220
Cartan subalgebra, maximally compact      222
Cauchy hypersurface      134
Cauchy — Szegoe kernel      283
Cayley transform      72
Chain      115
Chain approximation property      116
Characteristic function      11
Characterization of the global Lie wedges      41
Characterization of the Lie algebras with invariant cones      193
Compactly embedded element in a Lie algebra      178
Compactly embedded subalgebra      178
Comparable      115
Complex flag manifolds      221
Complex polarization      231
Compression semigroup      203
Conal curve, infinite      131
Conal homogeneous space      121
Conal homogeneous space, regular      138
Conal manifold      120
Conal order      123
Cone field, global      126
Cone field, regular      121 138
Cone potential      186
Conformal equivalence class      21
Contraction semigroup      63
Control system on G      173
Control system, invariant      173
Controllable      173
Core of      5 168
Curve, conal      123
Curve, W-conal      123
Derived representation      262
Dual wedge      2
Edge of the wedge      2
Element, generic      235
Equianalyticity Lemma      264
Existence Theorem for maximizing curves      145
Expansion semigroup      63
Exposed face      3 81
Extended affine triangle      62
Face      3
Face of a semigroup      81
Formal dimension      287
Forward set      114
Free group theorem      101
Frobenius — Perron group      170
Fubini study metric      217
Function, $\theta$-positive      126
Function, strictly W-positive      39
Fundamental group      91
Gauss kernel, complex      288
Gauss kernel, real      288
Gaussian function, complex      288
Gaussian function, real      288
generating      2
Global in G      29
Globally hyperbolic      116
Globally orderable      126
Group action, free      95
Group action, Hamiltonian      210
Group action, proper      95
Group of units      19
Group with cocompact radical      171
Hamiltonian vector field      209
Heat equation      36
Highest weight      219
Hilton's Lemma for monoids      95
Hofmann — Ruppert Arc Theorem      86
Hofmann's Theorem on hyperplane subalgebras      164
Holomorphic contraction representation      265
Holomorphic discrete series      272
Holomorphic mapping      257
Homogeneous coordinates      217
Homogeneous space, unimodular      140
Hyperplane subalgebra of abelian type      163
Hyperplane subalgebra of simple type      163
Hyperplane subalgebra of solvable type      163
Invariant      19
Invariant control set      203
Invariant semigroup      26
Involutive semigroup      254
Isotropy group      18
Krein space      226
Lawson's Theorem on Maximal Subsemigroups      172
Lawson's Theorem on Ol'shanskii semigroups      198
Left ordered group      29
Left reversible      109
Length functional of C      15
Lie algebra, $\Delta$-reduced      162
Lie algebra, dual symmetric      194
Lie algebra, symmetric      194
Lie face      83
Lie generating      19
Lie group, symmetric      194
Lie semigroup      20
Lie wedge      19
Lie wedge, associated symmetric      196
Lie wedge, global      29
Lie wedge, symmetric      195
Lie wedge, weakly global      29
Locally convex      117
Lorentz cone      14
Lorentz group      121
Lorentzian cone      121
Lorentzian form      21
Main Theorem on Compression Semigroups      245
Main Theorem on Infinitesimally Generated Semigroups      157
Main Theorem on Representations of Half Planes      261
Maximal cone      188
Maximality Theorem for Complex Ol'shanskii Semigroups      253
Mid-reversible      109
Minimal cone      188
Minkowski space      121
Moderate growth      35
Moment map      210
Moment mapping      215
Monoid      19
Nice subspace      87
Norm-determining set      257
Normal exposed face      81
Ol'shanskii semigroups      200
Ol'shanskii wedge      195
Olshanskii semigroup      59
Olshanskii's Theorem on Hardy spaces      277
Order convex      117
Order interval      114
Oscillator group      76
Paneitz's Convexity Theorem      239
Parabolic subalgebra      218
Parabolic subgroup      220
Parking ramp      75
Pointed      2
Poisson bracket      210
Positive system      182 218
Positive system, t-adapted      182
Pospace      114
Proper      95
Pseudo-unitary group      226
Quasiorder, directed      108
Quasiorder, filtered      108
Reach      116
Reachable set      173
Representation, holomorphic      268
Representation, pseudo-unitary      226
Reproducing kernel Hilbert space      282
Reversible      109
Right reversible      109
Root, compact      182
Root, non-compact      182
Roots      182
Ruppert's Theorem      111
San Martin's Theorem      206
Semigroup, completely infinitesimally generated      153
Semigroup, infinitesimally generated      153
Semigroup, semitopological      254
Semisimple module      9
Siegel domain      288
Siegel upper halfplane      288
Spectral measure      257
Standard Lorentzian cone      22
Stone's theorem      260
Strong cone potential      189
Subalgebra, isotropic      231
Subsemigroup, maximal      164
Subsemigroup, open      166
Subsemigroup, reduced      168
Subsemigroup, total      165
Tangent wedge      19
Temporal semigroup      69
The Classification Theorem for invariant cones      193
The Covering Theorem for Conal Homogeneous Spaces      137
The Covering Theorem for Groups      150
The Extension Theorem      267
The Globality Theorem      128
The Invariance Theorem for Vector Fields      154
The Lie Semigroup Criterion      160
The Pseudo-unitary Trick      228
The Structure Theorem for Lie algebras with cone potential      187
The Swallowing Lemma      164
The Unit Group Theorem      148
The Units Neighborhood Theorem      149
Theorem of Luescher and Mack      292
Trace class operator      287
Vector field, temporal      68
Vietoris topology      114
wedge      2
Wedge (cone) field      120
Wedge fields, constant      121
Wedge, controllable      173
Wedge, regular      196
Weight lattice      220
Weight separating      235
Weights      219
Weyl group      219
Whirlpot      74
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