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Author : Onorato Timothy O'Meara
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 41,9 Mb
Release : 1974
Category : Mathematics
ISBN : 0821888692
Author : O. T. O'Meara
Publisher : Unknown
Page : 87 pages
File Size : 40,9 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:859818000
Author : Benjamin Klopsch,Nikolay Nikolov,Christopher Voll
Publisher : Cambridge University Press
Page : 175 pages
File Size : 42,8 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9781139495653
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
Author : Derek John Scott Robinson
Publisher : World Scientific
Page : 210 pages
File Size : 41,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9810210485
This solution booklet is a supplement to the book ?A Course in Linear Algebra with Applications?. It will be useful to lecturers and to students taking the subject since it contains complete solutions to all 283 exercises in the book.
Author : Pavel I. Etingof,Olivier Schiffmann
Publisher : Unknown
Page : 242 pages
File Size : 45,5 Mb
Release : 2010
Category : Mathematical physics
ISBN : 1571462074
Author : Robinson
Publisher : Allied Publishers
Page : 442 pages
File Size : 48,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8177644521
Author : John W. Lawrence,Frank A. Zorzitto
Publisher : Cambridge University Press
Page : 639 pages
File Size : 50,8 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9781108836654
A lucid guide to abstract algebra, this comprehensive textbook provides in depth coverage for upper undergraduate students.
Author : Jing-Song Huang
Publisher : World Scientific
Page : 206 pages
File Size : 50,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9810237251
This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.
Author : Roger William Carter
Publisher : Unknown
Page : 190 pages
File Size : 53,8 Mb
Release : 1995-08-17
Category : Mathematics
ISBN : 0521499224
An excellent introduction to the theory of Lie groups and Lie algebras.
Author : Robert Steinberg
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 43,6 Mb
Release : 2016-12-22
Category : Algebraic geometry -- Algebraic groups -- Algebraic groups
ISBN : 9781470431051
Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967–1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added.
Author : Roger William Carter,Graeme Segal,Ian Grant Macdonald
Publisher : Unknown
Page : 190 pages
File Size : 42,8 Mb
Release : 1995
Category : Mathematics
ISBN : 0521495792
In this excellent introduction to the theory of Lie groups and Lie algebras, three of the leading figures in this area have written up their lectures from an LMS/SERC sponsored short course in 1993. Together these lectures provide an elementary account of the theory that is unsurpassed. In the first part Roger Carter concentrates on Lie algebras and root systems. In the second Graeme Segal discusses Lie groups. And in the final part, Ian Macdonald gives an introduction to special linear groups. Anybody requiring an introduction to the theory of Lie groups and their applications should look no further than this book.
Author : J. F. Adams
Publisher : University of Chicago Press
Page : 192 pages
File Size : 50,9 Mb
Release : 1982
Category : Mathematics
ISBN : 9780226005300
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
Author : Hsiang Wu-yi
Publisher : World Scientific
Page : 160 pages
File Size : 46,5 Mb
Release : 2017-04-07
Category : Mathematics
ISBN : 9789814740739
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive "tour of revisiting" the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces. With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books. We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius–Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1–4). It is a wonderful reality of the Lie theory that the clear-cut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semi-simple theory, as well as that of the symmetric spaces (cf. Lectures 5– 9). This is the main reason that makes the succeeding generalizations to the semi-simple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward.
Author : Onorato Timothy O'Meara
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 49,7 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821815168
This volume, the sequel to the author's ""Lectures on Linear Groups"", is the definitive work on the isomorphism theory of symplectic groups over integral domains. Recently discovered geometric methods which are both conceptually simple and powerful in their generality are applied to the symplectic groups for the first time. There is a complete description of the isomorphisms of the symplectic groups and their congruence subgroups over integral domains.Illustrative is the theorem $\mathrm{PSp}_n(\mathfrak o)\cong\mathrm{PSp}_{n_1}(\mathfrak o_1)\Leftrightarrow n=n_1$ and $\mathfrak o\cong\mathfrak o_1$ for dimensions $\geq 4$. The new geometric approach used in the book is instrumental in extending the theory from subgroups of $\mathrm{PSp})n(n\geq6)$ where it was known to subgroups of $\mathrm{P}\Gamma\mathrm{Sp}_n(n\geq4)$ where it is new. There are extensive investigations and several new results on the exceptional behavior of $\mathrm{P}\Gamma\mathrm{Sp}_4$ in characteristic 2. The author starts essentially from scratch (even the classical simplicity theorems for $\mathrm{PSp}_n(F)$ are proved) and the reader need be familiar with no more than a first course in algebra.
Author : E.B. Vinberg
Publisher : Birkhäuser
Page : 151 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892742
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
