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Author: François Digne
Publisher: Cambridge University Press
Published: 2020-03-05
Total Pages: 267
ISBN-13: 1108481485
DOWNLOAD EBOOKAn up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Author: Brian Hall
Publisher: Springer
Published: 2015-05-11
Total Pages: 452
ISBN-13: 3319134671
DOWNLOAD EBOOKThis 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
Author: Alexander A. Kirillov
Publisher: Cambridge University Press
Published: 2008-07-31
Total Pages: 237
ISBN-13: 0521889693
DOWNLOAD EBOOKThis book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author: Charles Benedict Thomas
Publisher: Imperial College Press
Published: 2004
Total Pages: 158
ISBN-13: 9781860944840
DOWNLOAD EBOOKThis book provides an introduction to representations of both finite and compact groups. The proofs of the basic results are given for the finite case, but are so phrased as to hold without change for compact topological groups with an invariant integral replacing the sum over the group elements as an averaging tool. Among the topics covered are the relation between representations and characters, the construction of irreducible representations, induced representations and Frobenius reciprocity. Special emphasis is given to exterior powers, with the symmetric group Sn as an illustrative example. The book concludes with a chapter comparing the representations of the finite group SL2(p) and the non-compact Lie group SL2(P).
Author: Dmitriĭ Petrovich Zhelobenko
Publisher: American Mathematical Soc.
Published: 1973-01-01
Total Pages: 464
ISBN-13: 9780821886649
DOWNLOAD EBOOKAuthor: M. F. Atiyah
Publisher: Cambridge University Press
Published: 1979
Total Pages: 349
ISBN-13: 0521226368
DOWNLOAD EBOOKIn 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.
Author: Barry Simon
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 280
ISBN-13: 0821804537
DOWNLOAD EBOOKThis text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.
Author: Brian C. Hall
Publisher: Springer Science & Business Media
Published: 2003-08-07
Total Pages: 376
ISBN-13: 9780387401225
DOWNLOAD EBOOKThis book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.
Author: William Fulton
Publisher: Springer Science & Business Media
Published: 1991
Total Pages: 616
ISBN-13: 9780387974958
DOWNLOAD EBOOKIntroducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.
Author: James E. Humphreys
Publisher: Cambridge University Press
Published: 2006
Total Pages: 260
ISBN-13: 9780521674546
DOWNLOAD EBOOKA comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
