Lie Methods In Deformation Theory
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Lie Methods In Deformation Theory
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Author : Marco Manetti
language : en
Publisher:
Release Date : 2022
Lie Methods In Deformation Theory written by Marco Manetti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer-Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book. .
Lie Methods In Deformation Theory
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Author : Marco Manetti
language : en
Publisher: Springer Nature
Release Date : 2022-08-01
Lie Methods In Deformation Theory written by Marco Manetti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-01 with Mathematics categories.
This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
Maurer Cartan Methods In Deformation Theory
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Author : Vladimir Dotsenko
language : en
Publisher: Cambridge University Press
Release Date : 2023-09-07
Maurer Cartan Methods In Deformation Theory written by Vladimir Dotsenko 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 2023-09-07 with Mathematics categories.
A unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics.
Deformation Theory Of Discontinuous Groups
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Author : Ali Baklouti
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-17
Deformation Theory Of Discontinuous Groups written by Ali Baklouti and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
This project is a second edition of the textbook: Deformation Theory of Discontinuous Groups (De Gruyter 2022). It is devoted to studying various geometric and topological concepts related to the deformation and moduli spaces of discontinuous group actions, and building some interrelationships between these concepts. It presents full proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and researchers in Lie theory, discontinuous groups, and deformation spaces. A part of the first edition, the setting of affine actions is introduced and new ideas and methods are developed with full proofs. The setting of compact extensions is also re-written with new approaches and proofs. It also contains the most recent developments of the theory, extending from basic concepts to a comprehensive exposition, and highlighting the newest approaches and methods in deformation theory. It also includes the most recent solutions to many open questions over the last decades and brings related newest research results in this area. For specialists and beginners in deformation theory, the settings of Heisenberg and Threadlike cases are differently re-written with full details and proofs.
Generalized Lie Theory In Mathematics Physics And Beyond
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Author : Sergei D. Silvestrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-18
Generalized Lie Theory In Mathematics Physics And Beyond written by Sergei D. Silvestrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-18 with Mathematics categories.
This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.
Algebraic Operads
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Author : Jean-Louis Loday
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-08
Algebraic Operads written by Jean-Louis Loday and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-08 with Mathematics categories.
In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.
Geometric And Topological Methods For Quantum Field Theory
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Author : Sylvie Paycha
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Geometric And Topological Methods For Quantum Field Theory written by Sylvie Paycha 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 2007 with Mathematics categories.
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
Deformation Theory Of Algebras And Structures And Applications
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Deformation Theory Of Algebras And Structures And Applications written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).
Homology And Cohomology A Primer For Undergraduates Through Applications
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Author : Luca Vitagliano
language : en
Publisher: World Scientific
Release Date : 2025-04-14
Homology And Cohomology A Primer For Undergraduates Through Applications written by Luca Vitagliano and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-14 with Mathematics categories.
The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergraduate Mathematics students, as well as graduate and postgraduate students in other fields, particularly Theoretical Physics, who require a highly compact overview of this vast theory. The book also explores how (co)homology theory naturally arises in seemingly unrelated areas of Mathematics.The theory is presented from scratch, requiring no prerequisites other than basic linear algebra, point-set topology, and calculus. The presentation is simple, concise, yet rigorous, making it accessible to undergraduate Mathematics and likely Physics students from the third year onward. The book emphasizes the theory's numerous applications across Algebra and Geometry, rather than focusing solely on the theoretical aspects. The pedagogical approach of this book, complemented by examples and exercises, sets it apart from standard textbooks in Homological Algebra and Algebraic Topology. The end-of-chapter problems offer insight into more advanced material and serve as a tool for testing comprehension of the theory.After having gone through these lecture notes, the reader will be ready to tackle more specialized and advanced subjects such as Homological Algebra, Homotopy Theory, and Algebraic Topology.
Group Theoretical Methods In Physics
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Author : G.S Pogosyan
language : en
Publisher: CRC Press
Release Date : 2005-05-01
Group Theoretical Methods In Physics written by G.S Pogosyan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-01 with Mathematics categories.
Symmetry is permeating our understanding of nature: Group theoretical methods of intrinsic interest to mathematics have expanded their applications from physics to chemistry and biology. The ICGTMP Colloquia maintain the communication among the many branches into which this endeavor has bloomed. Lie group and representation theory, special functions, foundations of quantum mechanics, and elementary particle, nuclear, atomic, and molecular physics are among the traditional subjects. More recent areas include supersymmetry, superstrings and quantum gravity, integrability, nonlinear systems and quantum chaos, semigroups, time asymmetry and resonances, condensed matter, and statistical physics. Topics such as linear and nonlinear optics, quantum computing, discrete systems, and signal analysis have only in the last few years become part of the group theorists' turf. In Group Theoretical Methods in Physics, readers will find both review contributions that distill the state of the art in a broad field, and articles pointed to specific problems, in many cases, preceding their formal publication in the journal literature.