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Yetter-Drinfel`d Hopf Algebras over Groups of Prime Order, Sommerhäuser Yorck



: 3459.
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: 30 2022
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: Sommerhäuser Yorck
 Yetter-Drinfel`d Hopf Algebras over Groups of Prime Order
ISBN: 9783540437994
: Springer
:

ISBN-10: 3540437991
/: Paperback
: 162
: 0.55 .
: 09.07.2002
: Lecture Notes in Mathematics
: English
: References, indexes
: 23.62 x 15.75 x 0.99
: Professional & vocational
: Link
:
: : 235x155
: Researchers and graduate students in algebra andmathematical physics
: Hopf algebra
Radford Biproduct
Yetter-Drinfel'd module
classification
: eng
: Introduction.- Preliminaries.- Clifford theory.- Examples.- Isomorphisms.- Constructions.- Commutative Yetter-Drinfel'd Hopf algebras.- 7.Cocommutative Yetter-Drinfel'd Hopf algebras.- Semisimple Hopf algebras of dimension p3.- Semisimple Hopf algebras of dimension pq.- Applications.- References.- Subject index.- Symbol index.





Hopf Algebras

: Eiichi Abe
: Hopf Algebras
ISBN: 0521604893 ISBN-13(EAN): 9780521604895
: Cambridge Academ
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: 7668 .
  : .

: The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivans proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.

New Directions in Hopf Algebras

: Edited by Susan Montgomery
: New Directions in Hopf Algebras
ISBN: 0521815126 ISBN-13(EAN): 9780521815123
: Cambridge Academ
:
: 17256 .
  : .

: This timely collection of expository papers by leading researchers in the field highlights progress and new directions in Hopf algebras. The volume arises from the MSRI workshop on Hopf Algebras in October 1999, where many exciting recent developments were discussed. The work presented here will be stimulating to researchers and accessible to graduate students. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to recent work in quantum groups. In particular, there are chapters on recent progress in classifying finite-dimensional Hopf algebras, both in the semisimple case and in the pointed case, as well as what is known about the extension theory of Hopf algebras and on important connections of Hopf algebras to Lie algebras, knot theory and operator algebras. The volume also includes Mitsuhiro Takeuchis article A short course on quantum matrices, now a standard reference in spite of its relative lack of availability; it has been updated for this volume.

New Directions in Hopf Algebras

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: New Directions in Hopf Algebras
ISBN: 052112431X ISBN-13(EAN): 9780521124317
: Cambridge Academ
:
: 5203 .
  : .

: This book contains survey articles for graduate students and researchers on various topics surrounding Hopf algebras.

Cohomology of Drinfeld Modular Varieties

: Laumon
: Cohomology of Drinfeld Modular Varieties
ISBN: 0521109906 ISBN-13(EAN): 9780521109901
: Cambridge Academ
:
: 7805 .
  : .

: This book follows the author`s first volume on Drinfeld modular varieties, and is pitched at graduate students.

Cohomology of Drinfeld Modular Varieties

: Laumon
: Cohomology of Drinfeld Modular Varieties
ISBN: 0521172748 ISBN-13(EAN): 9780521172745
: Cambridge Academ
:
: 6572 .
  : .

: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.

Harmonic Functions on Groups and Fourier Algebras

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: Harmonic Functions on Groups and Fourier Algebras
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: Springer
: 4037 .
  : .

: This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

Elements of Mathematics / Lie Groups and Lie Algebras: Chapters 7-9

: Bourbaki Nicolas, Pressley A.N.
: Elements of Mathematics / Lie Groups and Lie Algebras: Chapters 7-9
ISBN: 3540434054 ISBN-13(EAN): 9783540434054
: Springer
:
: 11544 .
  : .

: This is the English translation of Bourbaki's text Groupes et Algèbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (3-540-42650-7) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

Elements of Mathematics. Lie Groups and Lie Algebras / Chapters 4-6

: Bourbaki Nicolas, Pressley A.
: Elements of Mathematics. Lie Groups and Lie Algebras / Chapters 4-6
ISBN: 3540426507 ISBN-13(EAN): 9783540426509
: Springer
:
: 11544 .
  : .

: From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems". A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite independent of Lie theory. The choice of such an approach makes for an elegant, self-contained treatment of some highly interesting mathematics, which can be read with profit and with relative ease by a very wide circle of readers (and with delight by many, if the reviewer is at all representative)."(G.B. Seligman in MathReviews)

Lie Algebras and Lie Groups / 1964 Lectures given at Harvard University

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ISBN: 3540550089 ISBN-13(EAN): 9783540550082
: Springer
:
: 4037 .
  : .

: This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.

Operator Algebras and Quantum Statistical Mechanics 1 / C*- and W*-Algebras. Symmetry Groups. Decomposition of States

: Bratteli Ola, Robinson Derek W.
: Operator Algebras and Quantum Statistical Mechanics 1 / C*- and W*-Algebras. Symmetry Groups. Decomposition of States
ISBN: 3540170936 ISBN-13(EAN): 9783540170938
: Springer
:
: 23099 .
  : .

: This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made.The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.

Lie Algebras and Algebraic Groups

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: Lie Algebras and Algebraic Groups
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: Springer
:
: 13859 .
  : .

: The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included.

Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

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: Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
ISBN: 1402025440 ISBN-13(EAN): 9781402025440
: Springer
:
: 12704 .
  : .

: Describes an original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. This book should is useful for researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications, as well as for other postgraduate and advanced graduate students in mathematics.


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