Deformation Theory of Algebras and Their Diagrams - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformation Theory of Algebras and Their Diagrams write by Martin Markl. This book was released on 2012. Deformation Theory of Algebras and Their Diagrams available in PDF, EPUB and Kindle. This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.
Deformation Theory of Algebras and Structures and Applications
Deformation Theory of Algebras and Structures and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformation Theory of Algebras and Structures and Applications write by Michiel Hazewinkel. This book was released on 2012-12-06. Deformation Theory of Algebras and Structures and Applications available in PDF, EPUB and Kindle. 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).
Deformation Theory and Quantum Groups with Applications to Mathematical Physics
Deformation Theory and Quantum Groups with Applications to Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformation Theory and Quantum Groups with Applications to Mathematical Physics write by Murray Gerstenhaber. This book was released on 1992. Deformation Theory and Quantum Groups with Applications to Mathematical Physics available in PDF, EPUB and Kindle. Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang. Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on). One of the oldest forms of algebraic quantization amounts to the study of deformations of a commutative algebra A (of classical observables) to a noncommutative algebra A*h (of operators) with the infinitesimal deformation given by a Poisson bracket on the original algebra A. This volume grew out of an AMS--IMS--SIAM Joint Summer Research Conference, held in June 1990 at the University of Massachusetts at Amherst. The conference brought together leading researchers in the several areas mentioned and in areas such as ``q special functions'', which have their origins in the last century but whose relevance to modern physics has only recently been understood. Among the advances taking place during the conference was Majid's reconstruction theorem for Drinfel$'$d's quasi-Hopf algebras. Readers will appreciate this snapshot of some of the latest developments in the mathematics of quantum groups and deformation theory.
Deformations of Algebraic Schemes
Deformations of Algebraic Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformations of Algebraic Schemes write by Edoardo Sernesi. This book was released on 2007-04-20. Deformations of Algebraic Schemes available in PDF, EPUB and Kindle. This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.
Lie Methods in Deformation Theory
Lie Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Methods in Deformation Theory write by Marco Manetti. This book was released on 2022-08-01. Lie Methods in Deformation Theory available in PDF, EPUB and Kindle. 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.
