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$229.00
41. Symmetries and Recursion Operators
$106.87
42. Representation Theory of the Virasoro
$40.44
43. The Lie Algebras su(N): An Introduction
 
44. The root system of sign (1,0,1):
 
45. Equationally complete non-associative
$74.12
46. Geometry And Dynamics: International
$45.85
47. Evolution Algebras and their Applications

41. Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations (Mathematics and Its Applications)
by I.S. Krasil'shchik, P.H. Kersten
Paperback: 400 Pages (2010-11-02)
list price: US$229.00 -- used & new: US$229.00
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Asin: 904815460X
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This book is a detailed exposition of algebraic and geometricalaspects related to the theory of symmetries and recursion operatorsfor nonlinear partial differential equations (PDE), both in classicaland in super, or graded, versions. It contains an original theory ofFrölicher-Nijenhuis brackets which is the basis for aspecial cohomological theory naturally related to the equationstructure. This theory gives rise to infinitesimal deformations ofPDE, recursion operators being a particular case of such deformations.
Efficient computational formulas for constructing recursion operatorsare deduced and, in combination with the theory of coverings, lead topractical algorithms of computations. Using these techniques,previously unknown recursion operators (together with thecorresponding infinite series of symmetries) are constructed. Inparticular, complete integrability of some superequations ofmathematical physics (Korteweg-de Vries, nonlinearSchrödinger equations, etc.) is proved.
Audience: The book will be of interest to mathematicians andphysicists specializing in geometry of differential equations,integrable systems and related topics. ... Read more


42. Representation Theory of the Virasoro Algebra (Springer Monographs in Mathematics)
by Kenji Iohara, Yoshiyuki Koga
Hardcover: 476 Pages (2010-11-29)
list price: US$124.00 -- used & new: US$106.87
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Asin: 0857291599
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The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations.

Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. The authors organize fundamental results in a unified way and refine existing proofs. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widely believed to be true, are collated, and results which are known but not verified are proven, such as the corrected structure theorem of Fock modules in chapter eight.

This book will be of interest to a wide range of mathematicians and physicists from the level of graduate students to researchers.

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43. The Lie Algebras su(N): An Introduction
by Walter Pfeifer
Paperback: 116 Pages (2003-09-17)
list price: US$69.95 -- used & new: US$40.44
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Asin: 376432418X
Average Customer Review: 5.0 out of 5 stars
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Lie algebras are efficient tools for analyzing the properties of physical systems. Concrete applications comprise the formulation of symmetries of Hamiltonian systems, the description of atomic, molecular and nuclear spectra, the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the Lie algebras su(n). First, characteristic quantities such as structure constants, the Killing form and functions of Lie algebras are introduced. The properties of the algebras su(2), su(3) and su(4) are investigated in detail. Geometric models of the representations are developed. A lot of care is taken over the use of the term 'multiplet of an algebra'.The book features an elementary (matrix) access to su(N)-algebras, and gives a first insight into Lie algebras. Student readers should be enabled to begin studies on physical su(N)-applications, instructors will profit from the detailed calculations and examples. ... Read more

Customer Reviews (4)

4-0 out of 5 stars Really about time su(n) representaions like these were available
For me the su(2),su(3) material wasn't new.For me the su(2),su(3) material wasn't new.
I was grateful for the representation of su(4) and the structure constants.
The expansion of the Gell-Mann matrices is consistent with standard physic text
notation ( so the su(4) structure constants in Gordon Kane's "Modern Elementary Particle Physics" agree exactly).
The explanation of Young tableau is welcome andthe subgroup structures given
illuminate the Dynkin diagrams for these Lie algebras as well.
I find myself wishing this text were available in the 70's or 80's.
The exposition is clear and covers the material well.
One needs some modern algebra background and a familiarity with matrix representation notation.His explanation of how two so(n) groups are Hermitian in su(n) is something it took me years to figure out on my own!
I say this is a book well done and one that has been needed for a long time.
I would that he had expanded the book with an su(5) representations, structure constants
and sub-algebras
I was grateful for the representaion of su(4) and the structure constants.
The expansion of the Gell-Mann matrices is consistent with standard physic text notation ( so the su(4) structure constants in Gordon Kane's "Modern Elementry Particle Physics" agree exactly).
The explaination of Young tableau is welcome andthe subgroup structures givenilluninate the Dynkin diagrams for these Lie algebras as well.
I find myself wishing this text were available in the 70's or 80's.
The exposition is clear and covers the material well.
One needs some modern algebra backgrond and a familarity with matrix representaion notation.
His explaination of how two so(n) groups are Hermetian in su(n) is something it took me years to figure out on my own!
I say this is a book well done and one that has been needed for a long time.I would that he had expanded the book with an su(5) representations, structure constants and sub-algebras

5-0 out of 5 stars GREAT!
Great indtroductory book, very user friendly.It explains and shows in an easy to understand and simple way....lots of examples and explanations. EASY AND ENJOYABLE READ.

5-0 out of 5 stars Lie algebra demystified
A practical introduction to an esoteric topic which frightens many physics students.

This book presupposes little background mathematics and begins by defining lie alegebras and providing adequate examples. He then details some basic properties of finite dimensional lie algebras and offers several ways of "representing" them including the adjoint representation. From the beginning there is an emphasis on applications to quantum mechanics and I especially enjoyed the section on SU ( 2) and it's application to angular momentum operators. SU ( 3) and SU ( 4 ) are developed in due time in a logical and easy to understand format.

He also shows, in a simple way, how the tangent space of the identity of a lie group has a lie algebra structure which is useful in studying the group's local properties.

A very handy reference for those studying advanced quantum mechanics and particle physics yet basic enough for undergraduates to grasp the concepts.

5-0 out of 5 stars An excellent practical guide
This short book covers an important aspect that has been neglected by most textbooks on Lie algebras written for physicists, namely providing a comprehensible introduction for undergraduates based on detailed examples, computations and precise motivations, without having to develop the formal theory. This is not a textbook on Lie algebras in the usual sense, but a practical guide whose intention is to provide a solid comprehension of the main facts on (finite dimensional) Lie algebras used in physics. This justifies the choice of the objects analyzed, the compact real form su(N) of the Lie algebras sl(N,C), which constitute an essential tool in the study of the interacting boson model and nuclear rotational states. The topics covered by this book are quite modest (there are no general proofs and no development of classical problems like the classification of simple Lie algebras), and focuses on a detailed comment on the properties of simple algebras using mainly three Lie algebras, su(2),su(3) and su(4), before ennouncing the general case in the last chapter. However, this should not be understated, specially because the book explains carefully the usual notations (which change in the literature from author to author) and tries to clarify the reasons that justify the study of the formal theory.
The book is divided into six chapters, which we comment separately. The first chapter is a quick and effective overview on the basic properties of simple Lie algebras, namely the adjoint representation, the Killing form, representations and their reducibility. For the inner product the Dirac bracket notation is used. The concept of multiplets, which plays an essential role, is introduced at the end of this chapter. Chapter 2 begins with a short discussion of hermitian matrices, and introduces the Lie algebra su(N) in the usual way. The complexification of this algebra is shortly commented, as well as the generation of the algebra by means of operators. The structure constants over the standard basis are obtained, and as application the Killing form for su(N) is computed. It should be said that the notations used in this chapter have in mind the Gell-Mann matrices, which will be introduced later. Chapter 3 studies the fundamental facts concerning the rank one algebra su(2), and which will be central to later developments. The topics commented are generators of su(2), that is, the Pauli matrices, the quantum mechanical operators J of angular momentum, the su(2) multiplets and the irreducible (complex) representations. Further the tensor products (called "direct products") of these representations and their decomposition into irreducible components is commented. Many very detailed computations are presented, which illustrate clearly the procedure and its significance. Moreover the graphical method for the tensor product decomposition is developed,
The fourth chapter, devoted to the Lie algebra su(3), which cosntitutes in some sense the core of this book, actually develops the main aspects necessary to the description of global symmetry schemes for hadrons (without deeping into the actual classification, for this would require a basic knowledge of quantum field theory). The Lie algebra su(3) is introduced according Gell-Mann's notation. The step operators and states of su(3) are introduced, and the individual states and multiplicities are carefully constructed using graphical motivation (which actually corresponds to the standard application of the su(2)-triples). In order to formalize the construction, the Young tableaux are used (these constituting an essential tool for the analysis of the su(N) algebras). Special attention is devoted to the fundamental su(3)-multiplet (the quark representation 3) and its dual. This leads naturally to the introduction of the hypercharge Y (however no reference to the Gell-Mann-Nishijima formula is made). The (quadratic) Casimir operator of su(3) and its eigenvalues are analyzed, with explicit examples that point out the main properties of this invariant. The next section focuses on the tensor products of su(3)-multiplets, and develops also the graphical method to deduce the decomposition. A table presents some of these tensor products (for highest weights lower or equal to (2,1)). Again, this motivation is used to present the Young tableaux. Chapter 5 presents more or less the same topics for the rank three algebra su(4), and discusses the charm C (as a natural consequence of the quantum numbers discussed for su(3)). The multiplets and tensor products are reviewed (the diagrams are of exceptional quality and clarity), and the chapter finishes commenting on the standard Weyl basis (that is, the basis obtained from the root system of the corresponding algebra; this is the presentation that will be found in almost any book on Lie algebras). These facts are presented without proof, but serve to illustrate fundamental facts like the Cartan integers or the presentation by generators and relations that the interested reader will find in any standard text. Chapter six gives a recopilation of the basic facts of the su(N) algebras for arbitrary values of N (hermitian generators and multiplets, quadratic Casimir operator, etc). The bibliography presents some texts to profound the study. A little remark: the reference to Cornwell's book refers specifically to volume II, which deals with the theory of finite dimensional Lie algebras.
On balance I think this book is an excellent first contact with Lie algebras for those using them in physics, because of the lucid style and the clarity in the exposition. The very detailed calculations and step by step introduction of the material allow the readers not familiar with Lie algebras tobecome confident with the main facts they will find in any standard textbook, and which often discourages because of notational problems or implicit assumption of knowledge concerning the fundamental properties. Although the notation is mainly that used in physics literature, the examples and motivations introduced in this text will help the reader in the transition to other books using alternative notations. This work is a welcome reference for both beginners in Lie algebras for physics, as well as for instructors. ... Read more


44. The root system of sign (1,0,1): Dedicated to Professor Shigeo Nakano on his 60th birthday
by Kyoji Saito
 Unknown Binding: 108 Pages (1984)

Asin: B0007B9NAU
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45. Equationally complete non-associative algebras I,
by Tae-il Suh
 Unknown Binding: Pages (1967)

Asin: B0007IW846
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46. Geometry And Dynamics: International Conference in Honor of the 60th Anniversary of Alberto Verjovsky, Cuernavaca, Mexico, January 6-11, 2003 (Contemporary Mathematics)
Paperback: 197 Pages (2005-12)
list price: US$62.00 -- used & new: US$74.12
(price subject to change: see help)
Asin: 0821838512
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47. Evolution Algebras and their Applications (Lecture Notes in Mathematics)
by Jianjun Paul Tian
Paperback: 130 Pages (2007-11-08)
list price: US$59.95 -- used & new: US$45.85
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Asin: 3540742832
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Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to  some further research topics.

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