Structure Of The Standard Modules For The Affine Lie Algebra A Subscript 1 Superscript 1
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Structure Of The Standard Modules For The Affine Lie Algebra A Subscript 1 Superscript 1
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Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
language : en
Publisher:
Release Date : 1985
Structure Of The Standard Modules For The Affine Lie Algebra A Subscript 1 Superscript 1 written by Mathematical Sciences Research Institute (Berkeley, Calif.). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Homotopical Algebraic Geometry Ii Geometric Stacks And Applications
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Author : Bertrand Toën
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Homotopical Algebraic Geometry Ii Geometric Stacks And Applications written by Bertrand Toën and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
Introduction To Vassiliev Knot Invariants
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Author : S. Chmutov
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-24
Introduction To Vassiliev Knot Invariants written by S. Chmutov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
A detailed exposition of the theory with an emphasis on its combinatorial aspects.
Structure Of The Level One Standard Modules For The Affine Lie Algebras B Subscript L 1 F4 1 And G2 1
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Author : Frank Rimlinger
language : en
Publisher:
Release Date : 1987
Structure Of The Level One Standard Modules For The Affine Lie Algebras B Subscript L 1 F4 1 And G2 1 written by Frank Rimlinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Clifford algebras categories.
Quantizations Of Conical Symplectic Resolutions
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Author : Ben Webster
language : en
Publisher:
Release Date : 2016
Quantizations Of Conical Symplectic Resolutions written by Ben Webster and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Lectures On Tensor Categories And Modular Functors
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Author : Bojko Bakalov
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lectures On Tensor Categories And Modular Functors written by Bojko Bakalov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.
Homotopy Of Operads And Grothendieck Teichmuller Groups
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Author : Benoit Fresse
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-21
Homotopy Of Operads And Grothendieck Teichmuller Groups written by Benoit Fresse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Mathematics categories.
The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.
Lecture Notes In Algebraic Topology
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Author : James Frederic Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lecture Notes In Algebraic Topology written by James Frederic Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic andgeometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, someknowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstructiontheory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to presentproofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, andhomological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Tensor Categories
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Author : Pavel Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-08-05
Tensor Categories written by Pavel Etingof and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Mathematics categories.
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
The Topology Of Fibre Bundles
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Author : Norman Earl Steenrod
language : en
Publisher:
Release Date : 1951
The Topology Of Fibre Bundles written by Norman Earl Steenrod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Mathematics categories.
Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.