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: A. Rosenberg Название: Noncommutative Algebraic Geometry and Representations of Quantized Algebras ISBN: 0792335759 ISBN-13(EAN): 9780792335757 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text contains an introduction to the recently developed spectral theory of associative rings and Abelian categories. Its applications to the study of irreducible representations of classes of algebras which play an important part in modern mathematical physics are also included.
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: 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: 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: Kac Victor G Et Al Название: Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (2Nd Edition) ISBN: 981452218X ISBN-13(EAN): 9789814522182 Издательство: World Scientific Publishing Рейтинг: Цена: 85530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Автор: Kac Victor G Et Al Название: Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras (2Nd Edition) ISBN: 9814522198 ISBN-13(EAN): 9789814522199 Издательство: World Scientific Publishing Рейтинг: Цена: 33790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gℓ∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra.The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras -- such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations -- simplify and clarify the constructions of the first edition of the book.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of two-dimensional statistical models, and string theory.
Автор: Calvin C. Moore Название: Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics ISBN: 1461291305 ISBN-13(EAN): 9781461291305 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey`s mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild.
Автор: Fuchs/Schweigert Название: Symmetries, Lie Algebras and Representations ISBN: 0521541190 ISBN-13(EAN): 9780521541190 Издательство: Cambridge Academ Рейтинг: Цена: 88710.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Diamond Название: Automorphic Forms and Galois Representations ISBN: 1107693632 ISBN-13(EAN): 9781107693630 Издательство: Cambridge Academ Рейтинг: Цена: 61240.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This collection, the second of two volumes arising from an LMS-EPSRC Durham Symposium, explores the importance of automorphic forms and Galois representations in number theory. The expository articles and research papers within cover recent progress in anabelian geometry, p-adic Hodge theory, the Langlands program, and p-adic methods in number theory.
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