This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.
The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.
Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.
Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Автор: Hall Brian Название: Lie Groups, Lie Algebras, and Representations ISBN: 3319134663 ISBN-13(EAN): 9783319134666 Издательство: Springer Рейтинг: Цена: 50810.00 T Наличие на складе: Невозможна поставка. Описание:
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 Poincar -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
Автор: Francois Digne, Jean Michel Название: Representations of Finite Groups of Lie Type ISBN: 1108722628 ISBN-13(EAN): 9781108722629 Издательство: Cambridge Academ Рейтинг: Цена: 48570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The original edition of this book, written for beginning graduate students, was the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including chapters on Hecke algebras and Green functions.
Автор: Francois Digne, Jean Michel Название: Representations of Finite Groups of Lie Type ISBN: 1108481485 ISBN-13(EAN): 9781108481489 Издательство: Cambridge Academ Рейтинг: Цена: 116160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The original edition of this book, written for beginning graduate students, was the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including chapters on Hecke algebras and Green functions.
Автор: Didier Arnal, Bradley Currey Название: Representations of Solvable Lie Groups: Basic Theory and Examples ISBN: 1108428096 ISBN-13(EAN): 9781108428095 Издательство: Cambridge Academ Рейтинг: Цена: 155230.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph answers the need for a unified account of the basic theory of unitary group representations, combined with new results, in a style that is broadly accessible for both graduate students and researchers.
Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff Название: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras ISBN: 1470451743 ISBN-13(EAN): 9781470451745 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 82770.00 T Наличие на складе: Нет в наличии. Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Автор: Graham J. Leuschke, Frauke Bleher, Ralf Schiffler, Dan Zacharia Название: Representations of Algebras ISBN: 1470435764 ISBN-13(EAN): 9781470435769 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 116430.00 T Наличие на складе: Невозможна поставка. Описание: Contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held in August 2016, at Syracuse University. This volume includes three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories.
Автор: P. Dr?xler; G. Michler; C.M. Ringel Название: Computational Methods for Representations of Groups and Algebras ISBN: 3034897405 ISBN-13(EAN): 9783034897402 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A joint research project of algebraists from the universities of Antwerp, Biele- feld, Essen, Leeds, Paris VI and Trondheim on "Invariants and Representations of Algebras" has been supported from 1991 to 1997 by the European Union programmes "Science" and "Human Capital and Mobility", it was coordinated by Mme M. -P. Malliavin (Paris VI). Later, algebraists from the universities of Edinburgh, Ioannina, Murcia and Torun joined the collaboration. This network is now coordinated by C. M. Ringel (Bielefeld). It has received funds from the European Commission in order to organize four conferences as part of the pro- gramme "Training and Mobility of Researchers", to be held during the period 1997-1999 at Essen, Murcia, Bielefeld and Ioannina. The first Euroconference of this series took place at the University of Essen, April 1-4, 1997. It was devoted to "Computational Methods for Representations of Groups and Algebras" . The organizers were P. Draxler (Bielefeld) and G. Michler (Essen). This volume collects most of the material presented at the conference. There had been an additional introductory lecture by H. Gollan; it is not included here, since its contents is available in the lecture notes: P. Fleischmann, G. O. Michler, P. Roelse, J. Rosenboom, R. Staszewski, C. Wagner, M. Weller, "Linear algebra over small finite fields on parallel machines", Vorlesungen Fachbereich Math. Univ. Essen, 23 (1995). Together with these notes, this volume will provide a survey on the present state of art.
Автор: Ceccherini-Silberstein Tullio, Scarabotti Fabio, Tolli Filippo Название: Gelfand Triples and Their Hecke Algebras: Harmonic Analysis for Multiplicity-Free Induced Representations of Finite Groups ISBN: 3030516067 ISBN-13(EAN): 9783030516062 Издательство: Springer Рейтинг: Цена: 51230.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs.
Автор: R. Fioresi, F. Gavarini Название: Chevalley Supergroups ISBN: 0821853007 ISBN-13(EAN): 9780821853009 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 60060.00 T Наличие на складе: Невозможна поставка. Описание: "January 2012, volume 215, number 1014 (end of volume)."
Автор: Naihuan Jing, Kailash C. Misra Название: Representations of Lie Algebras, Quantum Groups and Related Topics ISBN: 1470436965 ISBN-13(EAN): 9781470436964 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 116430.00 T Наличие на складе: Невозможна поставка. Описание: Contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held in November 2016. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, and related topics.
Автор: Futorny Vyacheslav, Ovsienko Serge Название: Galois Algebras And Their Representations ISBN: 9814299227 ISBN-13(EAN): 9789814299220 Издательство: World Scientific Publishing Цена: 74970.00 T Наличие на складе: Поставка под заказ. Описание: The book provides a comprehensive overview of the theory of Galois algebras and their representations developed by the authors. It gives a unique treatment of the theory of Gelfand-Tsetlin modules for finite W-algebras, including the universal enveloping algebra of gl(n), a new treatment of an analog of the Gelfand-Kirillov Conjecture for finite W-algebras, and a description of important new theory of Galois algebras.The book will be of interests to those who specialize in Lie theory, Representation theory and Ring theory.
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