Loops in Group Theory and Lie Theory

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Author :
Publisher : Walter de Gruyter
ISBN 13 : 3110900580
Total Pages : 377 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Loops in Group Theory and Lie Theory by : Péter Nagy

Download or read book Loops in Group Theory and Lie Theory written by Péter Nagy and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Loops in Group and Lie Theory

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)

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Book Synopsis Loops in Group and Lie Theory by : Péter T. Nagy

Download or read book Loops in Group and Lie Theory written by Péter T. Nagy and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups and Lie Algebras I

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 364257999X
Total Pages : 241 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Lie Groups and Lie Algebras I by : V.V. Gorbatsevich

Download or read book Lie Groups and Lie Algebras I written by V.V. Gorbatsevich and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Langlands Correspondence for Loop Groups

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Author :
Publisher : Cambridge University Press
ISBN 13 : 0521854431
Total Pages : 5 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Langlands Correspondence for Loop Groups by : Edward Frenkel

Download or read book Langlands Correspondence for Loop Groups written by Edward Frenkel and published by Cambridge University Press. This book was released on 2007-06-28 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.

Lie Groups and Lie Algebras I

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9783540612223
Total Pages : 552 pages
Book Rating : 4.6/5 (122 download)

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Book Synopsis Lie Groups and Lie Algebras I by : V.V. Gorbatsevich

Download or read book Lie Groups and Lie Algebras I written by V.V. Gorbatsevich and published by Springer Science & Business Media. This book was released on 1996-12-18 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Lie Groups

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Author :
Publisher : MAA
ISBN 13 : 9780883857595
Total Pages : 194 pages
Book Rating : 4.8/5 (575 download)

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Book Synopsis Lie Groups by : Harriet Suzanne Katcher Pollatsek

Download or read book Lie Groups written by Harriet Suzanne Katcher Pollatsek and published by MAA. This book was released on 2009-09-24 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Lie Groups

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Author :
Publisher : Courier Dover Publications
ISBN 13 : 0486824535
Total Pages : 227 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Theory of Lie Groups by : Claude Chevalley

Download or read book Theory of Lie Groups written by Claude Chevalley and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Groups Beyond an Introduction

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Publisher : Springer Science & Business Media
ISBN 13 : 1475724535
Total Pages : 622 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Lie Groups Beyond an Introduction by : Anthony W. Knapp

Download or read book Lie Groups Beyond an Introduction written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.

Lectures on Lie Groups

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Author :
Publisher : World Scientific
ISBN 13 : 9789810235291
Total Pages : 118 pages
Book Rating : 4.2/5 (352 download)

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Book Synopsis Lectures on Lie Groups by : Wu Yi Hsiang

Download or read book Lectures on Lie Groups written by Wu Yi Hsiang and published by World Scientific. This book was released on 2000 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the maximal tori theorem of . Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clear-cut understanding of the orbital geometry.

Introduction to the Theory of Lie Groups

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Author :
Publisher : Springer
ISBN 13 : 331954375X
Total Pages : 300 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Introduction to the Theory of Lie Groups by : Roger Godement

Download or read book Introduction to the Theory of Lie Groups written by Roger Godement and published by Springer. This book was released on 2017-05-09 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.

Lie Groups, Lie Algebras, and Some of Their Applications

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Author :
Publisher : Courier Corporation
ISBN 13 : 0486131564
Total Pages : 610 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Lie Groups, Lie Algebras, and Some of Their Applications by : Robert Gilmore

Download or read book Lie Groups, Lie Algebras, and Some of Their Applications written by Robert Gilmore and published by Courier Corporation. This book was released on 2012-05-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Lie Groups and Lie Algebras I

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Author :
Publisher : Springer
ISBN 13 : 9783540186977
Total Pages : 238 pages
Book Rating : 4.1/5 (869 download)

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Book Synopsis Lie Groups and Lie Algebras I by : V.V. Gorbatsevich

Download or read book Lie Groups and Lie Algebras I written by V.V. Gorbatsevich and published by Springer. This book was released on 1993-04-15 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Ischia Group Theory 2010

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Author :
Publisher : World Scientific
ISBN 13 : 9814350052
Total Pages : 416 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Ischia Group Theory 2010 by : Mariagrazia Bianchi

Download or read book Ischia Group Theory 2010 written by Mariagrazia Bianchi and published by World Scientific. This book was released on 2012 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positive laws on generators in powerful pro-p groups / C. Acciarri and G.A. Fernandez-Alcober -- Periodic groups saturated by dihedral subgroups / B. Amberg and L. Kazarin -- A note on finite groups in which the conjugacy class sizes form an arithmetic progression / M. Bianchi, A. Gillio and P.P. Palfy -- A survey of recent progress on non-abelian tensor squares of groups / R.D. Blyth, F. Fumagalli and M. Morigi -- Conjugacy classes of subgroups of finite p-groups: the first gap / R. Brandl -- The Tutte polynomial of the Schreier graphs of the Grigorchuck group and the Basilica group / T. Ceccherini-Silberstein, A. Donno and D. Iacono -- On maximal subgroups of the alternating and symmetric groups / V. Colombo -- Markov's problems through the looking glass of Zariski and Markov topologies / D. Dikranjan and D. Toller -- Linear groups with finite dimensional orbits / M.R. Dixon, L.A. Kurdachenko and J. Otal -- Three-dimensional loops as sections in a four-dimensional solvable Lie group / A. Figula -- A note on finite p-groups with a maximal elementary subgroup of rank 2 / G. Glauberman -- Finitely generated free by C[symbol] pro-p groups / W. Herfort and P.A. Zalesskii -- Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M[symbol] / Z. Janko -- Twisted conjugacy in certain Artin groups / A. Juhasz -- Applications of Clifford's theorem to Frobenius groups of automorphisms / E.I. Khukhro -- Inducing [symbol]-partial characters with a given vertex / M.L. Lewis -- Groups and Lie rings with Frobenius groups of automorphisms / N. Yu. Makarenko -- On integral representations of finite groups / D. Malinin -- On p-groups of small powerful class / A. Mann -- Lifting (2, k)-generators of linear groups / A. Maroti and C. Tamburini Bellani -- Fixed point subgroups and character tables / G. Navarro -- Permutability and seriality in locally finite groups / D.J.S. Robinson -- On the exponent of a finite group with a four-group of automorphisms / E. Romano and P. Shumyatsky -- Examples of Markov chains on spaces with multiplicities / F. Scarabotti and F. Tolli -- On the order and the element orders of finite groups: results and problems / W.J. Shi -- On local finiteness of verbal subgroups in residually finite groups / P. Shumyatsky -- The adjoint group of radical rings and related questions / Ya. P. Sysak -- On the Gorenstein dimension of soluble groups / O. Talelli -- Decomposition numbers for projective modules of finite Chevalley groups / A.E. Zalesski

Loop Spaces, Characteristic Classes and Geometric Quantization

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817647317
Total Pages : 318 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Loop Spaces, Characteristic Classes and Geometric Quantization by : Jean-Luc Brylinski

Download or read book Loop Spaces, Characteristic Classes and Geometric Quantization written by Jean-Luc Brylinski and published by Springer Science & Business Media. This book was released on 2009-12-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Groups

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Publisher : Springer Science & Business Media
ISBN 13 : 1461480248
Total Pages : 532 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Lie Groups by : Daniel Bump

Download or read book Lie Groups written by Daniel Bump and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group Theory

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Author :
Publisher : Princeton University Press
ISBN 13 : 9781400837670
Total Pages : 288 pages
Book Rating : 4.8/5 (376 download)

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Book Synopsis Group Theory by : Predrag Cvitanović

Download or read book Group Theory written by Predrag Cvitanović and published by Princeton University Press. This book was released on 2008-07-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.

Lectures on Lie Groups

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Author :
Publisher : University of Chicago Press
ISBN 13 : 0226005305
Total Pages : 192 pages
Book Rating : 4.2/5 (26 download)

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Book Synopsis Lectures on Lie Groups by : J. F. Adams

Download or read book Lectures on Lie Groups written by J. F. Adams and published by University of Chicago Press. This book was released on 1982 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[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