Nilpotent Lie Algebras
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Author | : M. Goze |
Publisher | : Springer Science & Business Media |
Total Pages | : 350 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 9401724326 |
This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.
Author | : Veronique Fischer |
Publisher | : Birkhäuser |
Total Pages | : 568 |
Release | : 2016-03-08 |
Genre | : Mathematics |
ISBN | : 3319295586 |
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
Author | : Martin W. Liebeck |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 2012-01-25 |
Genre | : Mathematics |
ISBN | : 0821869205 |
This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
Author | : J. F. Humphreys |
Publisher | : Oxford University Press, USA |
Total Pages | : 296 |
Release | : 1996 |
Genre | : Language Arts & Disciplines |
ISBN | : 9780198534594 |
Each chapter ends with a summary of the material covered and notes on the history and development of group theory.
Author | : William.M. McGovern |
Publisher | : Routledge |
Total Pages | : 201 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351428691 |
Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.
Author | : David J. Winter |
Publisher | : Courier Corporation |
Total Pages | : 162 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 048646282X |
Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition.
Author | : Maria Gorelik |
Publisher | : Springer Nature |
Total Pages | : 553 |
Release | : 2019-10-18 |
Genre | : Mathematics |
ISBN | : 3030235319 |
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Author | : Libor Šnob |
Publisher | : American Mathematical Soc. |
Total Pages | : 306 |
Release | : 2017-04-05 |
Genre | : |
ISBN | : 147043654X |
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain classes of nilpotent and solvable Lie algebras of arbitrary finite dimensions for which complete or partial classification exists and discuss in detail their construction and properties. The book is based on material that was previously dispersed in journal articles, many of them written by one or both of the authors together with their collaborators. The reader of this book should be familiar with Lie algebra theory at an introductory level.
Author | : Roger William Carter |
Publisher | : Cambridge University Press |
Total Pages | : 662 |
Release | : 2005-10-27 |
Genre | : Mathematics |
ISBN | : 9780521851381 |
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author | : Nathan Jacobson |
Publisher | : Courier Corporation |
Total Pages | : 348 |
Release | : 2013-09-16 |
Genre | : Mathematics |
ISBN | : 0486136795 |
DIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div