Generalized Lie theory in mathematics, physics and beyond:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783540853329 |
| DOI: | 10.1007/978-3-540-85332-9 |
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Datensatz im Suchindex
| _version_ | 1804139004517416960 |
|---|---|
| adam_text | CONTENTS PART I NON-ASSOCIATIVE AND NON-COMMUTATIVE STRUCTURES FOR
PHYSICS 1 MOUFANG TRANSFORMATIONS AND NOETHER CURRENTS 3 EUGEN PAAL 1.1
INTRODUCTION 3 1.2 MOUFANG LOOPS AND MAL TSEV ALGEBRAS 4 1.3
BIREPRESENTATIONS 4 1.4 MOUFANG-NOETHER CURRENTS AND ETC 6 REFERENCES 8
2 WEAKLY NONASSOCIATIVE ALGEBRAS, RICCATI AND KP HIERARCHIES 9
ARISTOPHANES DIMAKIS AND FOLKERT MIILLER-HOISSEN 2.1 INTRODUCTION 9 2.2
NONASSOCIATIVITY AND KP 10 2.3 A CLASS OF WNA ALGEBRAS AND A MATRIX
RICCATI HIERARCHY 13 2.4 WNA ALGEBRAS AND SOLUTIONS OF THE DISCRETE KP
HIERARCHY 17 2.5 FROM WNA TO GELFAND-DICKEY-SATO 20 2.6 CONCLUSIONS 23
REFERENCES 24 3 APPLICATIONS OF TRANSVECTANTS 29 CHRIS ATHORNE 3.1
INTRODUCTION 29 3.2 TRANSVECTANTS 30 3.3 HIROTA 31 3.4 PADE 33 3.5
HYPERELLIPTIC 34 REFERENCES 36 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989665143 DIGITALISIERT DURCH X CONTENTS 4
AUTOMORPHISMS OF FINITE ORTHOALGEBRAS, EXCEPTIONAL ROOT SYSTEMS AND
QUANTUM MECHANICS 39 ARTUR E. RUUGE AND FRED VAN OYSTAEYEN 4.1
INTRODUCTION 39 4.2 SATURATED CONFIGURATIONS 41 4.3 NON-COLOURABLE
CONFIGURATIONS 41 4.4 THE E 6 CASE 42 4.5 ORTHOALGEBRAS GENERATED BY E%
43 4.6 CONCLUSIONS 45 REFERENCES 45 5 A REWRITING APPROACH TO GRAPH
INVARIANTS 47 LARS HELLSTROM 5.1 BACKGROUND 47 5.2 GRAPH THEORY 48 5.3
THE PROBLEM 50 5.4 SEMIGRAPHS 52 5.5 APPLYING THE DIAMOND LEMMA 58 5.6
CLASSIFICATION OF INVARIANTS 64 REFERENCES 67 PART II NON-COMMUTATIVE
DEFORMATIONS, QUANTIZATION, HOMOLOGICAL METHODS, AND REPRESENTATIONS 6
GRADED ^-DIFFERENTIAL ALGEBRA APPROACH TO ^-CONNECTION 71 VIKTOR ABRAMOV
6.1 INTRODUCTION 71 6.2 GRADED ^-DIFFERENTIAL ALGEBRA 72 6.3
^-CONNECTION AND ITS CURVATURE 73 6.4 MATRIX OF A ^-CONNECTION 75
REFERENCES 79 7 ON GENERALIZED N-COMPLEXES COMING FROM TWISTED
DERIVATIONS ... 81 DANIEL LARSSON AND SERGEI D. SILVESTROV 7.1
INTRODUCTION 81 7.2 GENERAL FRAMEWORK OF ( F)-DERIVATIONS 82 7.3
GENERALIZED AT-COMPLEXES AND AN EXAMPLE 86 REFERENCE CONTENTS XI 8.5
QUANTIZATIONS OF /^-MATRICES 95 REFERENCES 98 9 CONNECTIONS ON MODULES
OVER SINGULARITIES OF FINITE AND TAME CM REPRESENTATION TYPE 99 EIVIND
ERIKSEN AND TROND ST0LEN GUSTAVSEN 9.1 INTRODUCTION 99 9.2 PRELIMINARIES
100 9.3 OBSTRUCTION THEORY 102 9.4 RESULTS AND EXAMPLES 104 REFERENCES
107 10 COMPUTING NONCOMMUTATIVE GLOBAL DEFORMATIONS OF D-MODULES ... 1
09 EIVIND ERIKSEN 10.1 INTRODUCTION 109 10.2 NONCOMMUTATIVE GLOBAL
DEFORMATIONS OF D-MODULES 110 10.3 COMPUTING NONCOMMUTATIVE GLOBAL
DEFORMATIONS ILL 10.4 CALCULATIONS FOR D-MODULES ON ELLIPTIC CURVES 113
REFERENCES 117 11 COMPARING SMALL ORTHOGONAL CLASSES 119 GABRIELLA
D ESTE 11.1 INTRODUCTION 119 11.2 PRELIMINARIES 120 11.3 PROOFS AND
EXAMPLES 122 REFERENCES 128 PART III GROUPS AND ACTIONS 12 HOW TO
COMPOSE LAGRANGIAN? 131 EUGEN PAAL AND JIIRI VIRKEPU 12.1 INTRODUCTION
131 12.2 GENERAL METHOD FOR CONSTRUCTING LAGRANGIANS 132 12.3 LAGRANGIAN
FOR S0(2) 133 12.4 PHYSICAL INTERPRETATION 136 12.5 LAGRANGIAN FOR THE
AFFINE TRANSFORMATIONS OF THE LINE 136 REFERENCES 140 13 SEMIDIRECT
PRODUCTS OF GENERALIZED QUATERNION GROUPS B XII CONTENTS 14 A
CHARACTERIZATION OF A CLASS OF 2-GROUPS BY THEIR ENDOMORPHISM SEMIGROUPS
151 TATJANA GRAMUSHNJAK AND PEETER PUUSEMP 14.1 INTRODUCTION 151 14.2
THE GROUP G N 153 14.3 THE GROUP G 20 I 55 14.4 THE GROUP G 27 156
REFERENCES 158 15 ADJOINT REPRESENTATIONS AND MOVEMENTS 161 MAIDO RAHULA
AND VITALI RETSNOI 15.1 INTRODUCTION 161 15.2 GENERALIZED LEIBNITZ RULE
162 15.3 TANGENT GROUP 162 15.4 LINEAR GROUP GL(2,R) 163 15.5 THE
OPERATOR OF CENTER 165 15.6 DISCRIMINANT PARABOLA 166 15.7 RELATIONS TO
MOMENTS IN PROBABILITY THEORY 167 15.8 CONCLUSION 169 REFERENCES 170 16
APPLICATIONS OF HYPOCONTINUOUS BILINEAR MAPS IN INFINITE-DIMENSIONAL
DIFFERENTIAL CALCULUS 171 HELGE GLOCKNER 16.1 INTRODUCTION 171 16.2
PRELIMINARIES AND BASIC FACTS 172 16.3 DIFFERENTIABILITY PROPERTIES OF
COMPOSITIONS WITH HYPOCONTINUOUS BILINEAR MAPPINGS 178 16.4 HOLOMORPHIC
FAMILIES OF OPERATORS 180 16.5 LOCALLY CONVEX POISSON VECTOR SPACES 182
REFERENCES 186 PART IV QUASI-LIE, SUPER-LIE, HOM-HOPF AND SUPER-HOPF
STRUCTURES AND EXTENSIONS, DEFORMATIONS AND GENERALIZATIONS OF
INFINITE-DIMENSIONAL LI CONTENTS XIII 18 BOSONISATION AND PARASTATISTICS
207 K. KANAKOGLOU AND C. DASKALOYANNIS 18.1 INTRODUCTION AND DEFINITIONS
207 18.2 (SUPER-)LIE AND (SUPER-)HOPF ALGEBRAIC STRUCTURE OF THE
PARABOSONIC P 1 ^ AND PARAFERMIONIC ^ ALGEBRAS 208 18.3 BOSONISATION AS
A TECHNIQUE OF REDUCING SUPERSYMMETRY 212 18.4 DISCUSSION 217 REFERENCES
218 19 DEFORMATIONS OF THE WITT, VIRASORO, AND CURRENT ALGEBRA 219
MARTIN SCHLICHENMAIER 19.1 INTRODUCTION 219 19.2 DEFORMATIONS OF LIE
ALGEBRAS 221 19.3 KRICHEVER-NOVIKOV ALGEBRAS 223 19.4 THE GEOMETRIC
FAMILIES 226 19.5 THE GEOMETRIC BACKGROUND 229 19.6 EXAMPLES FOR THE
DEGENERATED SITUATIONS 230 REFERENCES 233 20 CONFORMAL ALGEBRAS IN THE
CONTEXT OF LINEAR ALGEBRAIC GROUPS .... 235 PAVEL KOLESNIKOV 20.1
INTRODUCTION 235 20.2 CATEGORIES OF CONFORMAL ALGEBRAS 237 20.3
ASSOCIATIVE ( GJ-CONFORMAL ALGEBRAS 240 20.4 CONFORMAL ENDOMORPHISM
ALGEBRA OVER A LINEAR ALGEBRAIC GROUP 243 REFERENCES 246 21 LIE COLOR
AND HOM-LIE ALGEBRAS OF WITT TYPE AND THEIR CENTRAL EXTENSIONS 247
GUNNAR SIGURDSSON AND SERGEI SILVESTROV 21.1 INTRODUCTION 247 21. 303
XIV CONTENTS PART V COMMUTATIVE SUBALGEBRAS IN NONCOMMUTATIVE ALGEBRAS
23 ALGEBRAIC DEPENDENCE OF COMMUTING ELEMENTS IN ALGEBRAS 265 SERGEI
SILVESTROV, CHRISTIAN SVENSSON, AND MARCEL DE JEU 23.1 INTRODUCTION 265
23.2 DESCRIPTION OF THE PROBLEM: COMMUTING ELEMENTS IN AN ALGEBRA ARE
GIVEN, THEN FIND CURVES THEY LIE ON 267 23.3 BURCHNALL-CHAUNDY
CONSTRUCTION FOR DIFFERENTIAL OPERATORS 269 23.4 BURCHNALL-CHAUNDY
THEORY FOR THE ^-DEFORMED HEISENBERG ALGEBRA 273 REFERENCES 279 24
CROSSED PRODUCT-LIKE AND PRE-CRYSTALLINE GRADED RINGS 281 JOHAN OINERT
AND SERGEI D. SILVESTROV 24.1 INTRODUCTION 281 24.2 PRELIMINARIES AND
DEFINITIONS 282 24.3 THE COMMUTANT OF A) IN A CROSSED PRODUCT-LIKE RING
284 24.4 THE CENTER OF A CROSSED PRODUCT-LIKE RING AQO%M 286 24.5
INTERSECTION THEOREMS 288 24.6 EXAMPLES OF CROSSED PRODUCT-LIKE AND
CRYSTALLINE GRADED RINGS 292 REFERENCES 295 25 DECOMPOSITION OF THE
ENVELOPING ALGEBRA SO (5) 297 CESTMIR BURDFK AND ONDREJ NAVRATIL 25.1
INTRODUCTION 297 25.2 THE LIE ALGEBRA SO(5) 298 25.3 THE HIGHEST WEIGHT
VECTORS 299 25.4 CONCLUSION 302 REFERENCES 302 INDEX
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| spelling | Generalized Lie theory in mathematics, physics and beyond Sergei Silvestrov ... ed. Berlin [u.a.] Springer 2009 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Lie-Theorie (DE-588)4251836-2 gnd rswk-swf Lie-Theorie (DE-588)4251836-2 s DE-604 Silvestrov, Sergei (DE-588)136773710 edt Erscheint auch als Druckausgabe 978-3-540-85331-2 https://doi.org/10.1007/978-3-540-85332-9 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017447195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Generalized Lie theory in mathematics, physics and beyond Lie-Theorie (DE-588)4251836-2 gnd |
| subject_GND | (DE-588)4251836-2 |
| title | Generalized Lie theory in mathematics, physics and beyond |
| title_auth | Generalized Lie theory in mathematics, physics and beyond |
| title_exact_search | Generalized Lie theory in mathematics, physics and beyond |
| title_full | Generalized Lie theory in mathematics, physics and beyond Sergei Silvestrov ... ed. |
| title_fullStr | Generalized Lie theory in mathematics, physics and beyond Sergei Silvestrov ... ed. |
| title_full_unstemmed | Generalized Lie theory in mathematics, physics and beyond Sergei Silvestrov ... ed. |
| title_short | Generalized Lie theory in mathematics, physics and beyond |
| title_sort | generalized lie theory in mathematics physics and beyond |
| topic | Lie-Theorie (DE-588)4251836-2 gnd |
| topic_facet | Lie-Theorie |
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