Автор: Steven Givant; Paul Halmos Название: Introduction to Boolean Algebras ISBN: 0387402934 ISBN-13(EAN): 9780387402932 Издательство: Springer Рейтинг: Цена: 6002.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Suitable for advanced undergraduates and beginning graduate students, this book treats Boolean algebras, develops some ideas, and provides insights. It includes explanation of the relationship between Boolean rings and Boolean algebras. It features chapters on topology and on continuous functions.
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: Di Vincenzo Onofrio Mario, Giambruno Antonio Название: Polynomial Identities in Algebras ISBN: 3030631133 ISBN-13(EAN): 9783030631130 Издательство: Springer Рейтинг: Цена: 23757.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems.
Автор: Leo Esakia; Guram Bezhanishvili; Wesley H. Hollida Название: Heyting Algebras ISBN: 3030120953 ISBN-13(EAN): 9783030120955 Издательство: Springer Рейтинг: Цена: 7965.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents an English translation of a classic Russian text on duality theoryfor Heyting algebras. Written by Georgian mathematician Leo Esakia, the text provedpopular among Russian-speaking logicians. This translation helps make the ideasaccessible to a wider audience and pays tribute to an influential mind in mathematicallogic. The book discusses the theory of Heyting algebras and closure algebras, aswell as the corresponding intuitionistic and modal logics. The author introduces thekey notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripkeframes), resulting in the structures now known as Esakia spaces. The main theoremsinclude a duality between the categories of closure algebras and of hybrids, and a dualitybetween the categories of Heyting algebras and of so-called strict hybrids.Esakia’s book was originally published in 1985. It was the first of a planned two-volume monographon Heyting algebras. But after the collapse of the Soviet Union, the publishing houseclosed and the project died with it. Fortunately, this important work now lives on inthis accessible translation. The Appendix of the book discusses the planned contentsof the lost second volume.
Автор: Oleg K. Sheinman Название: Current Algebras on Riemann Surfaces ISBN: 3110263963 ISBN-13(EAN): 9783110263961 Издательство: Walter de Gruyter Цена: 18985.00 р. Наличие на складе: Нет в наличии.
Описание: This monograph is an introduction into a new and fast developing field on the crossroads of infinite-dimensional Lie algebra theory and contemporary mathematical physics. It contains a self-consistent presentation of the theory of Krichever-Novikov algebras, Lax operator algebras, their interaction, representation theory, relations to moduli spaces of Riemann surfaces and holomorphic vector bundles on them, to Lax integrable systems, and conformal field theory. For beginners, the book provides a short way to join in the investigations in these fields. For experts, it sums up the recent advances in the theory of almost graded infinite-dimensional Lie algebras and their applications.The book may serve as a base for semester lecture courses on finite-dimensional integrable systems, conformal field theory, almost graded Lie algebras. Majority of results are presented for the first time in the form of monograph.
Автор: Abe Shenitzer; I.L. Kantor; A.S. Solodovnikov Название: Hypercomplex Numbers ISBN: 1461281911 ISBN-13(EAN): 9781461281917 Издательство: Springer Рейтинг: Цена: 14673.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: If we put z = al + a2i, z` = b+ bi, 1 2 then we can rewrite (1) as The last identity states that "the product of a sum of two squares by a sum of two squares is a sum of two squares.
Автор: Kurt Luoto; Stefan Mykytiuk; Stephanie van Willige Название: An Introduction to Quasisymmetric Schur Functions ISBN: 1461472997 ISBN-13(EAN): 9781461472995 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Поставка под заказ.
Описание: An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theory of Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them.
The second goal is to give a survey of results with respect to an exciting new basis of the Hopf algebra of quasisymmetric functions, whose combinatorics is analogous to that of the renowned Schur functions.
Описание: This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.
Автор: Bogdan Ion, Siddhartha Sahi Название: Double Affine Hecke Algebras and Congruence Groups ISBN: 1470443260 ISBN-13(EAN): 9781470443269 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10659.00 р. Наличие на складе: Нет в наличии.
Автор: Witherspoon, Sarah J. Название: Hochschild cohomology for algebras ISBN: 1470449315 ISBN-13(EAN): 9781470449315 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 13444.00 р. Наличие на складе: Нет в наличии.
Описание: This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.
Автор: V.Kac Название: Infinite-Dimensional Lie Algebras, ISBN: 0521466938 ISBN-13(EAN): 9780521466936 Издательство: Cambridge Academ Рейтинг: Цена: 9029.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This is the third, substantially revised edition of this important monograph and graduate text. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems. The theory has applications in many areas of mathematics and mathematical physics and these are discussed in relation to the basic theory where appropriate.
Описание: General Notation.- 1 Prologue: The Algebraic Approach to Quantum Theories.- 2 ∗-Algebras.- 3 O*-Algebras.- 4 ∗-Representations.- 5 Positive Linear Functionals.- 6 Representations of Tensor Algebras.- 7 Integrable Representations of Commutative ∗-Algebras.- 8 The Weyl Algebra and the Canonical Commutation Relation.- 9 Integrable Representations of Enveloping Algebras.- 10 Archimedean Quadratic Modules and Positivstellensдtze.- 11 The Operator Relation XX*=F(X*X).- 12 Induced ∗-Representations.- 13 Well-behaved ∗-Representations.- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space.- B C*-Algebras and Representations.- C Locally Convex Spaces and Separation of Convex Sets.- References.- Symbol Index.- Subject Index.
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