A Generalization Of Massey Products With Applications To Deformation Theory
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Noncommutative Deformation Theory
Author | : Eivind Eriksen |
Publisher | : CRC Press |
Total Pages | : 382 |
Release | : 2017-09-19 |
Genre | : Mathematics |
ISBN | : 1351652125 |
Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields.
Deformation Theory of Algebras and Structures and Applications
Author | : Michiel Hazewinkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 1024 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9400930577 |
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).
Cohomology Operations and Applications in Homotopy Theory
Author | : Robert E. Mosher |
Publisher | : Courier Corporation |
Total Pages | : 226 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 0486466647 |
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Cubical Homotopy Theory
Author | : Brian A. Munson |
Publisher | : Cambridge University Press |
Total Pages | : 649 |
Release | : 2015-10-06 |
Genre | : Mathematics |
ISBN | : 1107030250 |
A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Higher Structures in Geometry and Physics
Author | : Alberto S. Cattaneo |
Publisher | : Springer Science & Business Media |
Total Pages | : 371 |
Release | : 2010-11-25 |
Genre | : Mathematics |
ISBN | : 081764735X |
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Hopf Algebras and Tensor Categories
Author | : Nicolás Andruskiewitsch |
Publisher | : American Mathematical Soc. |
Total Pages | : 347 |
Release | : 2013-02-21 |
Genre | : Mathematics |
ISBN | : 0821875647 |
This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4-8, 2011, at the University of Almeria, Almeria, Spain. The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other topics discussed in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, relations to the conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.