TAILIEUCHUNG - Đề tài " The classification of pcompact groups for p odd "

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. . | Annals of Mathematics The classification of p-compact groups for p odd By K. K. S. Andersen J. Grodal J. M. M0ller and A. Viruel Annals of Mathematics 167 2008 95 210 The classification of p-compact groups for p odd By K. K. S. Andersen J. Grgdal J. M. Mgller and A. ViRUEL Abstract A p-compact group as defined by Dwyer and Wilkerson is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope and later the conjecture that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture for p an odd prime proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last and rather intricate piece namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd. Contents 1. Introduction Relationship to the Lie group case and the conjectural picture for p 2 Organization of the paper Notation Acknowledgements 2. Skeleton of the proof of the main Theorems and 3. Two lemmas used in Section 2 4. The map T Aut BX Aut BNX 5. Automorphisms of maximal torus normalizers 6. Reduction to connected center-free simple p-compact groups The first named author was supported by EU grant EEC HPRN-CT-1999-00119. The second named author was supported by NSF grant DMS-0104318 a Clay Liftoff Fellowship and the Institute for Advanced Study for different parts of the time this research was carried out. The fourth named author was supported by EU grant EEC HPRN-CT-1999-00119 FEDER-MEC grant MTM2007-60016 and by the JA grants FQM-213 and FQM-2863. 96 K. K. S. ANDERSEN J. GRODAL J. M. M0LLER AND A. VIRUEL 7. An integral version of a theorem of Nakajima .

• Thạc sĩ - Tiến sĩ - Cao học
• classification
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Standard Practice for classification of soils
• Standard Practice for classification of soil aggregate
• Highway construction
• Soil aggregate mixtures for highway construction purposes
• Soil mixtures for highway construction purposes
• Description of classification groups soil
• Definition classification essay
• Function classification essay
• Classification organization
• How to proceed
• language focus
• Learning English
• Multi label classification for physical activity recognition
• Various accelerometer sensor positions
• The Label Combination
• Multi class classification approaches
• Several state of the art traditional multi class classification approache
• Noisy image classification using hybrid deep learning methods
• Noisy image classification
• Hybrid deep learning methods
• The input noisy image
• The DNN based better noisy image classification system
• Urban classification
• Spatial resolution
• Data transformations
• Vietnam’s urban classification
• Urban classification maps
• Remote sensing
• Land use pattern
• Supervised classification
• Classification accuracy
• Kappa coefficient
• Unsupervised and supervised classification
• Command area
• D 7 shahapur branch canal
• Unsupervised classification using Landsat 8 Imagery
• Unsupervised classification for land
• Imbalanced data classification
• Data mining
• Hybrid method
• Cancer data classification
• Effectiveness of cancer data classification
• Synthetic Minority Over sampling Technique
• Information and communication technology
• Multilabel over sampling
• Class alignment for imbalanced multilabel text classification
• Imbalanced multilabel text classification
• Multilabel text classification
• Class imbalance problem
• Validation assessments on resampling method in imbalanced binary classification
• Linear discriminant analysis
• Imbalanced binary classification
• Resampling method
• Class imbalance
• Binary classification
• Classification and Prediction
• Classification with decision tree
• Artificial Neural Networksm
• Algorithm for decision tree induction
• Attribute Selection Measure
• Computer Security
• Role Based Access Control
• Role Classification Algorithm
• Algorithm Preliminaries
• Algorithm Training Phase
• Algorithm Classification Phase
• Feature selection
• Feature ranking methods
• Classification algorithms
• Naive Bayes
• RBF network
• International Journal of Computer Networks and Communications
• A study on analysis of sms classification
• TF IDF weighting
• Vector space model
• The classification accuracy
• International Journal of Computer Networks and Communications Security
• Land cover classification using hidden markov models
• Land cover classification
• Hidden markov models
• Multispectral satellite images
• Modulus of elasticity
• Classification technique
• RA AF classification process
• Concrete damage classification
• Acoustic emission setup
• International Journal of computer science & communication networks
• SVD based dimensionality reduction for efficient web page classification
• SVD based dimensionality reduction
• Efficient web page classification
• Effective pre processing
• Singular value decomposition
• Safety classification of systems structures
• Components for pool type research reactors
• Pool type research reactors
• The SSCs following the safety classification
• Earth Sciences
• TAS classification
• Volcanic rocks
• Plutonic rocks
• Chemical classification
• Correct statistical analysis of compositional data
• Land uses
• Characterization and classification
• Classification of soils
• Soils under lower Brahmaputra valley
• Seven soil profiles
• Feature vector
• Support vector machine
• Text classification
• Text classification based
• Development of the Internet has increased
• Pesticides classification
• Impact on environment
• WHO classification
• Moderately dangerous
• Slightly dangerous
• BMC Pediatrics
• Cerebral palsy
• Gross motor function classification system
• Classification systems
• Paediatric physiotherapist
• Coconut inventory
• Mapping using object oriented classification
• Oriented classification
• SVM Classifier
• KNN classifier
• Object oriented classification
• K Nearest neighbour
• Rulebased classification
• Shoolagiri and surroundings