Mathematics
Lie Groups and Algebra


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Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groups
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Oxford Graduate Texts in Mathematics #5: Lie Groups: An Introduction Through Linear Groups
by Wulf Rossman

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Includes bibliographical references (p. 258-260) and index....
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Lie Groups (Universitext)
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Lie Groups (Universitext)
by Claudio Procesi

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Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups...
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Lie Algebras of Bounded Operators
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Lie Algebras of Bounded Operators
by Daniel Beltija

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There is a fruitful and fascinating interaction between infinite dimensional operator theory (particularly decomposable, scalar and spectral generalized operator theory due to C. Foias and I. Colojoara) and Lie algebra theory. The present book is the...
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Progress in Mathematics #243: Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday
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Progress in Mathematics #243: Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday
by Joseph Bernstein

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Dedicated to Anthony Joseph in honor of his 60th birthday, this volume contains two articles reviewing different aspects of Joseph's impact on the theory of representations of Lie algebras and 17 original contributions from leading specialists in...
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Semi-Simple Lie Algebras and Their Representations
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Semi-Simple Lie Algebras and Their Representations
by Robert N Cahn

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Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Subjects include simple roots and...
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Lie Algebras and Algebraic Groups
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Lie Algebras and Algebraic Groups
by Patrice Tauvel

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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...
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Lie Groups for Pedestrians 2ND Edition
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Lie Groups for Pedestrians 2ND Edition
by Harry Lipkin

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This book shows how the well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin; the three-dimensional harmonic oscillator; algebras of operators that change the number of particles; permutations...
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Lie Theory: Lie Algebras and Representations
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Lie Theory: Lie Algebras and Representations
by Jean Philippe Anker

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Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title "Lie Theory," feature...
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Progress in Mathematics #229: Lie Theory: Unitary Representations, Number Theory, and Compactifications
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Progress in Mathematics #229: Lie Theory: Unitary Representations, Number Theory, and Compactifications
by Jean Philippe Anker

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Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature...
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Graduate Texts in Mathematics #225: Lie Groups
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Graduate Texts in Mathematics #225: Lie Groups
by Daniel Bump

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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...
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The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov
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The Orbit Method in Geometry and Physics: In Honor of A.A. Kirillov
by Christian Duval

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The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and...
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Lie Equations Volume 1 General Theory
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Lie Equations Volume 1 General Theory
by Antonio Kumpera

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As the title indicates, the content of these notes is a lengthy construction of techniques devised to study specific differential geometric problems. In this introduction we state our main objectives and illustrate by examples some of their geometric...
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Princeton Mathematical Series #45: Cohomological Induction and Unitary Representations (PMS-45)
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Princeton Mathematical Series #45: Cohomological Induction and Unitary Representations (PMS-45)
by Anthony Knapp

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This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a...
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Introduction To Lie Algebras and Representation Theory (72 Edition)
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Introduction To Lie Algebras and Representation Theory (72 Edition)
by James E. Humphreys

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This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms...
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Lie Groups Beyond an Introduction 2ND Edition
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Lie Groups Beyond an Introduction 2ND Edition
by Anthony Knapp

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This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. New to the second edition is material about tools through which the representation theory of compact groups plays a...
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Annals of Mathematics Studies #118: Unitary Representations of Reductive Lie Groups. (Am-118)
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Annals of Mathematics Studies #118: Unitary Representations of Reductive Lie Groups. (Am-118)
by David A Vogan

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This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete...
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Abstract Lie Algebras
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Abstract Lie Algebras
by David J. Winter

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Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. It also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Contents...
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Lie Algebras
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Lie Algebras
by Nathan Jacobson

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Definitive treatment covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, and more. Classic handbook for researchers and students; useable...
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Lie Groups, Lie Algebras, and Some of Their Applications
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Lie Groups, Lie Algebras, and Some of Their Applications
by Robert Gilmore

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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...
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Progress in Mathematics #0123: Lie Theory and Geometry
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Progress in Mathematics #0123: Lie Theory and Geometry
by Jean Brylinski

Synopsis
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostanta (TM)s fundamental work in all...
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