Formal Groups And Applications

Author : Michiel Hazewinkel
Publisher : American Mathematical Soc.
ISBN 13 : 082185349X
Total Pages : 603 pages
Book Rating : 4.98/5 ( download)

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Download or read book Formal Groups and Applications written by Michiel Hazewinkel and published by American Mathematical Soc.. This book was released on 2012 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.

Author : Jean A. Dieudonne
Publisher : CRC Press
ISBN 13 : 1000723313
Total Pages : 286 pages
Book Rating : 4.11/5 ( download)

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Download or read book Introduction to the Theory of Formal Groups written by Jean A. Dieudonne and published by CRC Press. This book was released on 2020-01-29 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of formal Lie group was derived in a natural way from classical Lie theory by S. Bochner in 1946, for fields of characteristic 0. Its study over fields of characteristic p > 0 began in the early 1950’s, when it was realized, through the work of Chevalley, that the familiar “dictionary” between Lie groups and Lie algebras completely broke down for Lie algebras of algebraic groups over such a field. This volume, starts with the concept of C-group for any category C (with products and final object), but the author’s do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised: no algebraic geometry and very little commutative algebra is required in chapters I to III, and the algebraic geometry used in chapter IV is limited to the Serre- Chevalley type (varieties over an algebraically closed field).

Author : Justin Noel
Publisher :
ISBN 13 : 9781109315691
Total Pages : 91 pages
Book Rating : 4.94/5 ( download)

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Download or read book Some Applications of the Theory of Formal Groups to Algebraic Topology written by Justin Noel and published by . This book was released on 2009 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: We also provide a reinterpretation of McClure's conditions in the language of formal group laws.

Author : Douglas C. Ravenel
Publisher : American Mathematical Society
ISBN 13 : 1470472937
Total Pages : 417 pages
Book Rating : 4.31/5 ( download)

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Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Society. This book was released on 2023-02-09 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.

Author : Lindsay Childs
Publisher : American Mathematical Soc.
ISBN 13 : 0821810774
Total Pages : 133 pages
Book Rating : 4.74/5 ( download)

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Download or read book Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders written by Lindsay Childs and published by American Mathematical Soc.. This book was released on 1998 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9781556080036
Total Pages : 540 pages
Book Rating : 4.34/5 ( download)

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Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

Author : Società italiana di fisica
Publisher : IOS Press
ISBN 13 : 1614992134
Total Pages : 652 pages
Book Rating : 4.34/5 ( download)

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Download or read book Quantum Groups and Their Applications in Physics written by Società italiana di fisica and published by IOS Press. This book was released on 1996 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on quantum groups, i.e., continuous deformations of Lie groups, and their applications in physics. These algebraic structures have been studied in the last decade by a growing number of mathematicians and physicists, and are found to underlie many physical systems of interest. They do provide, in fact, a sort of common algebraic ground for seemingly very different physical problems. As it has happened for supersymmetry, the q-group symmetries are bound to play a vital role in physics, even in fundamental theories like gauge theory or gravity. In fact q-symmetry can be considered itself as a generalization of supersymmetry, evident in the q-commutator formulation. The hope that field theories on q-groups are naturally reguralized begins to appear founded, and opens new perspectives for quantum gravity. The topics covered in this book include: conformal field theories and quantum groups, gauge theories of quantum groups, anyons, differential calculus on quantum groups and non-commutative geometry, poisson algebras, 2-dimensional statistical models, (2+1) quantum gravity, quantum groups and lattice physics, inhomogeneous q-groups, q-Poincaregroup and deformed gravity and gauging of W-algebras.

Author : K. Lonsted
Publisher : Springer
ISBN 13 : 3540350497
Total Pages : 664 pages
Book Rating : 4.91/5 ( download)

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Download or read book Algebraic Geometry written by K. Lonsted and published by Springer. This book was released on 2006-11-15 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Not long ago, conducting child assessment was as simple as stating that "the child gets along with others" or "the child lags behind his peers." Today's pediatric psychologists and allied professionals, by contrast, know the critical importance of using accurate measures with high predictive quality to identify pathologies early, form precise case conceptualizations, and provide relevant treatment options. Assessing Childhood Psychopathology and Developmental Disabilities provides a wide range of evidence-based methods in an immediately useful presentation from infancy through adolescence. Noted experts offer the most up-to-date findings in the most pressing areas, including: Emerging trends, new technologies, and implementation issues. Interviewing techniques and report writing guidelines. Intelligence testing, neuropsychological assessment, and scaling methods for measuring psychopathology. Assessment of major pathologies, including ADHD, conduct disorder, bipolar disorder, and depression. Developmental disabilities, such as academic problems, the autism spectrum and comorbid pathology, and self-injury. Behavioral medicine, including eating and feeding disorders as well as pain management. This comprehensive volume is an essential resource for the researcher's library and the clinician's desk as well as a dependable text for graduate and postgraduate courses in clinical child, developmental, and school psychology. (A companion volume, Treating Childhood Psychopathology and Developmental Disabilities, is also available to ensure greater continuity on the road from assessment to intervention to outcome.)

Author : Peter S. Landweber
Publisher : Springer
ISBN 13 : 3540393005
Total Pages : 232 pages
Book Rating : 4.09/5 ( download)

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Download or read book Elliptic Curves and Modular Forms in Algebraic Topology written by Peter S. Landweber and published by Springer. This book was released on 2006-11-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology. The resulting papers range, fom these topics through to quantum field theory, with considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.

Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937951
Total Pages : 967 pages
Book Rating : 4.57/5 ( download)

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Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt: