1 edition of **Noncompact Lie Groups and Some of Their Applications** found in the catalog.

- 93 Want to read
- 23 Currently reading

Published
**1994**
by Springer Netherlands, Imprint, Springer in Dordrecht
.

Written in English

- Group theory,
- Mathematics,
- Topological groups,
- Global analysis,
- Algebra

This book contains lectures presented by outstanding mathematicians and mathematical physicists at the NATO Advanced Research Workshop on noncompact Lie groups held in San Antonio, Texas in January 1993. It touches almost every important topics in the modern theory of representations of noncompact Lie groups and Lie algebras, Lie supergroups and Lie superalgebras, and quantum groups. It also includes several of the applications of this theory. The articles are exceptionally well written, ranging from expository articles easily accessible to graduate students to research articles for specialists which provide the most recent developments in this field -- some of which are being published for the first time here. The book also provides a coherent and readable introduction which reviews the underlying theory and defines the fundamental and relevant terms for the reader. The text is an outstanding source of material for mathematicians and mathematical physicists who are working or are planning to work in the field of representation theories of Lie groups, Lie supergroups and quantum groups.

**Edition Notes**

Statement | edited by Elizabeth A. Tanner, Raj Wilson |

Series | NATO ASI Series, Series C: Mathematical and Physical Sciences, 1389-2185 -- 429, NATO ASI series -- 429. |

Contributions | Wilson, Raj |

Classifications | |
---|---|

LC Classifications | QA252.3 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (512 pages). |

Number of Pages | 512 |

ID Numbers | |

Open Library | OL27077495M |

ISBN 10 | 9401110786 |

ISBN 10 | 9789401110785 |

OCLC/WorldCa | 840308795 |

analysis". For compact Lie groups, the analytic issues are easily dealt with, but become much trickier in the non-compact case. The Peter-Weyl theorem says that representations of compact Lie groups behave very much like representa-tions of nite groups, with the analytic issues similar to those that occur for Fourier series. The proper Lorentz group L p is a noncompact Lie group, and the SO(4) group is a compact Lie group. Two groups have the same Lie algebra but their real Lie algebras are different. In this chapter the irreducible representations of the proper Lorentz group is studied through those of the SO(4) group.

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their cat-egories of representations. Eventually these notes will consist of three chapters, each about pages long, and a short appendix. BibTeX information: @misc{milneLAG,File Size: 1MB. Erratum: Geometric Langlands duality and representations of algebraic groups over commutative rings [Annals of Mathematics, , 3, () ()] Doi: /annals I Mirkovic, K Vilonen.

( views) Advances in Discrete Differential Geometry by Alexander I. Bobenko (ed.) - Springer, This is the book on a newly emerging field of discrete differential geometry. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. , Lie groups, Lie algebras, and some of their applications Wiley New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be .

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Noncompact Lie Groups and Some of Their Applications book Lie Groups and Some of Their Applications (Nato Science Series C: (Closed)) Softcover reprint of the original 1st ed. Edition by Elizabeth A. Tanner (Editor) ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of Format: Paperback. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications.

The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are Brand: Springer Netherlands.

Cite this chapter as: Tanner E.A., Wilson R. () Noncompact Lie Groups, their Algebras and some of their Applications. In: Tanner E.A., Wilson R. (eds) Noncompact Lie Groups and Some of Their : Elizabeth A.

Tanner, Raj Wilson. Noncompact Lie Groups and Some of Their Applications, (NATO ASI Series, Kluwer Academic Publishers, Dordrecht, ) p. Cite as: arXiv [quant-ph] (or arXivv1 [quant-ph] for this version)Cited by: 1. Noncompact Lie Groups and Some of Their Applications, (NATO ASI Series, Kluwer Academic Publishers, Dordrecht, ) p.

Bibliographic Code: arXivI. Next after that, I bought online the excellent book of Hall, Lie Groups, Lie Algebras and Representations, edited by Springer-Verlag, that I am currently and profitably reading. Thanks, prof.

Gilmore, for a waste of money (29,95 USD) and several tens of unprofitable hours (plus thirty minutes to write and post this review).Cited by: Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics.

Many examples of Lie groups and Lie algebras are given throughout the text. Many years ago I wrote the book Lie Groups, Lie Algebras, and Some of Their Applications (NY: Wiley, ).

That was a big book: long and diﬃcult. Over the course of the years I realized that more than 90% of the most useful material in that book could be presented in less than 10% of the space. This realization was accompanied by a promiseFile Size: KB. "This book gives an introduction on the graduate level to the subject of Lie groups, Lie algebras and their representation theory.

The presentation is well organized and clear. this book is a very interesting and valuable addition to the list of already existing books on Lie groups." (J. Mahnkopf, Monatshefte für Mathematik, Vol. (3 Brand: Springer-Verlag New York. equations, and their applications range from quantum mechanics to meteo-rology.

Although inﬁnite-dimensional Lie groups have been investigated for quite some time, the scope of applicability of a general theory of such groups is still rather limited.

The main reason for this is that inﬁnite-dimensional Lie groups exhibit very peculiar features. This book is intended for a one year graduate course on Lie groups and Lie algebras.

The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture.

For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori. This is a book about arithmetic subgroups of semisimple Lie groups, which means that we will discuss the group SL(n;Z), and certain of its subgroups.

By de nition, the subject matter combines algebra (groups of matrices) with number theory (properties of the integers). However, it also has important applications in geometry. of real simple noncompact Lie groups. In this paper we discuss first the classification of all real simple Lie groups and then single out those classes which contain the Lorentz group.

' I PRELIMINARIES It is well known that the properties of Lie groups are intimately connected with the properties of Lie Size: KB. Compact Lie groups.

Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups include.

the circle group T and the torus groups T n,; the orthogonal groups O(n), the special orthogonal group SO(n) and its covering spin group Spin(n),; the unitary group U(n) and the special unitary group.

mannian symmetric spaces, Noncompact Lie groups and some of their applications, ed. E.A. Tanner et al, Kluwer (), 69– (with G. Heckman), Harmonic Analysis and Special Functions on Symmetric Spaces (book), Academic Press, San Diego, ().

(with R. Schimming), Helmholtz operators on harmonic manifolds, Acta Math. ( For Galois theory, there is a nice book by Douady and Douady, which looks at it comparing Galois theory with covering space theory etc. Another which has stood the test of time is Ian Stewart's book.

For Lie groups and Lie algebras, it can help to see their applications early on, so some of the text books for physicists can be fun to read. [7) R. Gilmore, Lie groups, Lie algebras, and some of their applications (Wiley, New York, ). - - [81 C- Wuifman, J. Chem Phys., to be published.

t compact, it is noncompact. Any Lie group generated by a set of operators Xk which close under commutation can be written as a product of one-parameter by: 7. With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications.

It further illustrates Lie group theory's role in expressing concepts and results from several fields of physics. edition. Includes 75 figures and 17 tables. Recent years an extensive literature appears using the Lie groups theory to solve the problems of computer vision. Lie groups theory is the natural representation of a space of transformations.

Varadarajan's little Cambridge book "intro to harmonic analysis on semi-simple Lie groups" is a relatively friendly intro to such things. Finite-dimensional repns theory, and repn theory of finite groups, does not give good hints about the sort of things that happen with non-compact, non-abelian, especially reductive, Lie groups!.

Noncompact Lie groups, their algebras and some of their applications, NATO Mathematical and Physical Sciences, C (), ; { E.A.

Tanner Mathematical Reviews, 95h (), ; 95h Noncompact Lie Groups and Some of their Applications, Proceedings of the NATO Advanced Research Workshop, { E.A. Tanner.This volume is a review on coherent states and some of their applications.

The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Quasi-Coherent States for Unitary Groups (B Skagerstam) “The book is clear proof of the exceptionally high.some types of noncompact complex abelian Lie groups and to classify all non-compact connected complex abelian Lie groups of dimension 3.

In a previous paper [5] we have constructed a complex Lie group, on which every holomorphic function is a constant and which contains no complex torus of positive dimension.