Loops in Group Theory and Lie Theory
Title | Loops in Group Theory and Lie Theory PDF eBook |
Author | Péter T. Nagy |
Publisher | Walter de Gruyter |
Pages | 384 |
Release | 2002 |
Genre | Mathematics |
ISBN | 9783110170108 |
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 Theory and Lie Theory
Title | Loops in Group Theory and Lie Theory PDF eBook |
Author | Péter Nagy |
Publisher | Walter de Gruyter |
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.
Loops in Group and Lie Theory
Title | Loops in Group and Lie Theory PDF eBook |
Author | Péter T. Nagy |
Publisher | |
Pages | 0 |
Release | 2002 |
Genre | Lie groups |
ISBN |
Langlands Correspondence for Loop Groups
Title | Langlands Correspondence for Loop Groups PDF eBook |
Author | Edward Frenkel |
Publisher | Cambridge University Press |
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.
Lie Groups, Lie Algebras, and Representations
Title | Lie Groups, Lie Algebras, and Representations PDF eBook |
Author | Brian Hall |
Publisher | Springer |
Pages | 452 |
Release | 2015-05-11 |
Genre | Mathematics |
ISBN | 3319134671 |
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Lie Groups and Lie Algebras I
Title | Lie Groups and Lie Algebras I PDF eBook |
Author | V.V. Gorbatsevich |
Publisher | Springer Science & Business Media |
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
Symmetries, Lie Algebras and Representations
Title | Symmetries, Lie Algebras and Representations PDF eBook |
Author | Jürgen Fuchs |
Publisher | Cambridge University Press |
Pages | 464 |
Release | 2003-10-07 |
Genre | Mathematics |
ISBN | 9780521541190 |
This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.