Loops In Group Theory And Lie Theory
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Author | : Péter Nagy |
Publisher | : Walter de Gruyter |
Total Pages | : 377 |
Release | : 2011-06-24 |
Genre | : Mathematics |
ISBN | : 3110900580 |
In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, topological geometry, and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.
Author | : Péter T. Nagy |
Publisher | : |
Total Pages | : 0 |
Release | : 2002 |
Genre | : Lie groups |
ISBN | : |
Author | : V.V. Gorbatsevich |
Publisher | : Springer Science & Business Media |
Total Pages | : 241 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 364257999X |
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter
Author | : Edward Frenkel |
Publisher | : Cambridge University Press |
Total Pages | : 5 |
Release | : 2007-06-28 |
Genre | : Mathematics |
ISBN | : 0521854431 |
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author | : V.V. Gorbatsevich |
Publisher | : Springer Science & Business Media |
Total Pages | : 552 |
Release | : 1996-12-18 |
Genre | : Mathematics |
ISBN | : 9783540612223 |
From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter
Author | : Harriet Suzanne Katcher Pollatsek |
Publisher | : MAA |
Total Pages | : 194 |
Release | : 2009-09-24 |
Genre | : Mathematics |
ISBN | : 9780883857595 |
This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called 'Putting the pieces together' in which all definitions and results are collected for reference and further reading is suggested.
Author | : Claude Chevalley |
Publisher | : Courier Dover Publications |
Total Pages | : 227 |
Release | : 2018-03-21 |
Genre | : Mathematics |
ISBN | : 0486824535 |
The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
Author | : Jean-Luc Brylinski |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2009-12-30 |
Genre | : Mathematics |
ISBN | : 0817647317 |
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.
Author | : Daniel Bump |
Publisher | : Springer Science & Business Media |
Total Pages | : 532 |
Release | : 2013-10-01 |
Genre | : Mathematics |
ISBN | : 1461480248 |
This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
Author | : J. F. Adams |
Publisher | : University of Chicago Press |
Total Pages | : 192 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : 0226005305 |
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky