Lectures on Representations of Locally Compact Groups, Ion Colojoara, Aurelian Gheondea

Автор: Monod, Nicolas (ecole Polytechnique Federale De Lausanne)
Название: New directions in locally compact groups
ISBN: 1108413129 ISBN-13(EAN): 9781108413121
Издательство: Cambridge Academ
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Описание: This collection of expository articles provides an overview of the major renaissance happening today in the study of locally compact groups and their many connections to other areas of mathematics, including geometric group theory, measured group theory and rigidity of lattices. For researchers and graduate students.

Автор: Carlo Garoni; Stefano Serra-Capizzano
Название: Generalized Locally Toeplitz Sequences: Theory and Applications
ISBN: 3319536788 ISBN-13(EAN): 9783319536781
Издательство: Springer
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Описание: Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications.

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
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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: Matthew J. Emerton
Название: Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups
ISBN: 0821875620 ISBN-13(EAN): 9780821875629
Издательство: Mare Nostrum (Eurospan)
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Описание: Provides the foundations for the locally analytic representation theory that is required in three of the author`s other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors.

Автор: Michel Enock; A. Connes; A. Ocneanu; Jean-Marie Sc
Название: Kac Algebras and Duality of Locally Compact Groups
ISBN: 3540547452 ISBN-13(EAN): 9783540547457
Издательство: Springer
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Цена: 121070.00 T
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Описание: Develops the category of Kac algebras that answers the original duality problem. This book is of interest to researchers working in quantum groups, particularly those interested in the approach by Lie groups and Lie algebras or by non-commutative geometry, and more generally also to those working in C* algebras or theoretical physics.

Автор: Ralph McKenzie; Matthew Valeriote
Название: Structure of Decidable Locally Finite Varieties
ISBN: 0817634398 ISBN-13(EAN): 9780817634391
Издательство: Springer
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Описание: Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]` but Tarski discovered these results around 1930).

Автор: Gene Freudenburg
Название: Algebraic Theory of Locally Nilpotent Derivations
ISBN: 3642067328 ISBN-13(EAN): 9783642067327
Издательство: Springer
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Описание: Invariant Theory and Algebraic Transformation Groups VII

Автор: Michel Enock; A. Connes; A. Ocneanu; Jean-Marie Sc
Название: Kac Algebras and Duality of Locally Compact Groups
ISBN: 3642081282 ISBN-13(EAN): 9783642081286
Издательство: Springer
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Описание: This book deals with the theory of Kac algebras and their dual- ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. . Kac and L. . Vajnermann in the seventies. The sub- ject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret- ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the character- ization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. . Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality.