TAILIEUCHUNG - Đề tài " On fusion categories "

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity). In particular the number of such categories (functors) realizing a. | Annals of Mathematics On fusion categories By Pavel Etingof Dmitri Nikshych and Viktor Ostrik Annals of Mathematics 162 2005 581 642 On fusion categories By Pavel Etingof Dmitri NiKSHycH and Viktor Ostrik Abstract Using a variety of methods developed in the literature in particular the theory of weak Hopf algebras we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive and that the S-matrix of any not necessarily hermitian modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple and that fusion categories and tensor functors between them are undeformable generalized Ocneanu rigidity . In particular the number of such categories functors realizing a given fusion datum is finite. Finally we develop the theory of Frobenius-Perron dimensions in an arbitrary fusion category. At the end of the paper we generalize some of these results to positive characteristic. 1. Introduction Throughout this paper except for 9 k denotes an algebraically closed field of characteristic zero. By a fusion category C over k we mean a k-linear semisimple rigid tensor monoidal category with finitely many simple objects and finite dimensional spaces of morphisms such that the endomorphism algebra of the neutral object is k see BaKi . Fusion categories arise in several areas of mathematics and physics - conformal field theory operator algebras representation theory of quantum groups and others. This paper is devoted to the study of general properties of fusion categories. This has been an area of intensive research for a number of years and many remarkable results have been obtained. However many of these results were proved not in general but under various assumptions on the category. The goal of this paper is to remove such assumptions and to give an account of the theory of fusion categories in full .

• Thạc sĩ - Tiến sĩ - Cao học
• categories
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research on choice behavior of beer categories brands
• Choice behavior of beer categories brands
• Beer categories brands
• Analyzing factors affecting
• The business process
• Livelihood pattern
• Gender wise livelihood pattern
• Various categories
• Farm families
• Various categories of farm families
• công nghệ thông tin
• tin học văn phòng
• mircrosoft office outlook 2003
• Working with Categories and Email
• make up
• mental operations
• The Scuola Operative Italiana
• metal categories
• Giullio Benedetti
• Minor categories
• Bamboo internodes
• container fauna
• volumetric capacity
• Detritus dynamics
• Efficient Unsupervised Discovery of Word Categories
• Symmetric Patterns
• High Frequency Words
• báo cáo khoa học
• mô hình ngôn ngữ
• xử lý ngôn ngữ tự nhiên
• Learning Semantic Categories
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• Mamoru Komachi Nara
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• Using linguistic principles
• recover empty categories
• Long Papers
• Tagging Inflective Languages
• Prediction
• Morphological Categories for a Rich
• Structured Tagset
• Improving Statistical
• Natural Language Translation
• Categories and Rules
• THE FORMAL CONSEQUENCES
• VARIABLES IN CCG CATEGORIES
• Beryl Hoffman
• Generative Power of CCGs
• Generalized Type Raised Categories
• Nobo Komagata
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• model language
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• Financial Assets
• Expense Categories
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• Main Balances
• Major Categories
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• AN EXTENDED LR PARSING
• ALGORITHM FOR GRAMMARS
• FEATURE BASED SYNTACTIC CATEGORIES
• Internal categories
• Simplicial groups
• Crossed modules
• Whiskered groupoids
• Peiffer elements
• Achillea L
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• Achillea maritima
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• Rural youth
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• Patan block of Jabalpur district
• Analyzing different categories
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• Rural youth regarding participation
• BMC Bioinformatics
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• Term similarity
• Cross categories
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• Milk production
• Studies on milk production
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• Different categories of farmers in four districts
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• Lecture Introduction to Business
• Bài giảng Nhập môn kinh doanh
• Business introduction
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• Categories of industrial goods
• increasing
• theory
• semantic
• mathematical
• applications
• Demographic Categories
• Informed Consent
• Complex Humanitarian
• Final Discussion