Algebraic Groups and their Representations, R.W. Carter; J. Saxl

Автор: R.W. Carter; J. Saxl
Название: Algebraic Groups and their Representations
ISBN: 0792352513 ISBN-13(EAN): 9780792352518
Издательство: Springer
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Цена: 208700.00 T
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Описание: Contains articles in the field of algebraic groups and related finite groups. This book includes articles on representation theory, tilting modules, canonical bases, endomorphism algebras, the symmetric group, the path model, homology bases, semisimplicity in prime characteristic, block theory, and Lusztig`s character formula.

Автор: A. Douady; J. M. G. Fell; L. Dal Soglio-Herault
Название: Induced Representations and Banach*-Algebraic Bundles
ISBN: 354008147X ISBN-13(EAN): 9783540081470
Издательство: Springer
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Цена: 32560.00 T
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Автор: David Arnold
Название: Abelian Groups and Representations of Finite Partially Ordered Sets
ISBN: 038798982X ISBN-13(EAN): 9780387989822
Издательство: Springer
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Цена: 130430.00 T
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Описание: Presents an exposition of connections between representations of finite partially ordered sets and abelian groups. This title emphasises on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible.

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
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Цена: 46570.00 T
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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: Marc Cabanes
Название: Finite Reductive Groups: Related Structures and Representations
ISBN: 0817638857 ISBN-13(EAN): 9780817638856
Издательство: Springer
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Цена: 135050.00 T
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Описание: This volume focuses on the representation theory of groups and related structures, combining the modular representation theory of finite groups of Richard Brauer and the representation theory of reductive groups of George Lusztig.

Автор: Kang Zuo
Название: Representations of Fundamental Groups of Algebraic Varieties
ISBN: 3540663126 ISBN-13(EAN): 9783540663126
Издательство: Springer
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Цена: 32560.00 T
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Описание: Using harmonic maps, non-linear PDE and techniques from algebraic geometry, this text enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.

Автор: Hall Brian
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 3319134663 ISBN-13(EAN): 9783319134666
Издательство: Springer
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Цена: 50810.00 T
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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: Anatoli Klimyk; Konrad Schm?dgen
Название: Quantum Groups and Their Representations
ISBN: 3642646018 ISBN-13(EAN): 9783642646010
Издательство: Springer
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Цена: 95770.00 T
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Описание: The invention of quantum groups is one of the outstanding achievements of mathematical physics and mathematics in the late twentieth century. The birth of the new theory and its rapid development are results of a strong interrelation between mathematics and physics. Quantu groups arose in the work of L.D. Faddeev and the Leningrad school on the inverse scattering method in order to solve integrable models. The algebra Uq(sh) appeared first in 1981 in a paper by P.P. Kulish and N.Yu. Reshetikhin on the study of integrable XYZ models with highest spin. Its Hopf algebra structure was discovered later by E.K. Sklyanin. A major event was the discovery by V.G. Drinfeld and M. Jimbo around 1985 of a class of Hopf algebras which can be considered as one-parameter deforma- tions of universal enveloping algebras of semisimple complex Lie algebras. These Hopf algebras will be called Drinfeld-Jimbo algebras in this book. Al- most simultaneously, S.L. Woronowicz invented the quantum group SUq(2) and developed his theory of compact quantum matrix groups. An algebraic approach to quantized coordinate algebras was given about this time by Yu.I. Manin.