E.B. Vinberg - Böcker
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7 produkter
1 960 kr
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In celebration of E. B. Dynkin's 70th birthday, this book presents current papers by those who participated in Dynkin's seminar on Lie groups and Lie algebras in the late 1950s and early 1960s. Dynkin had a major influence not only on mathematics, but also on the students who attended his seminar - many of whom are today's leading mathematicians in Russia and in the U.S. Dynkin's contributions to the theory of Lie groups is well known, and the survey paper by Karpelevich, Onishchik, and Vinberg allows readers to gain a deeper understanding of this work. Features several aspects of modern developments in Lie groups and Lie algebras, including...theory of invariants superalgebras arithmetic applications connections with mathematical physics. Providing insight on the extraordinary mathematical traditions that grew out of this important seminar, ""Lie Groups and Lie Algebras"" is a fitting celebration of Dynkin's achievements.
Del 20 - Encyclopaedia of Mathematical Sciences
Lie Groups and Lie Algebras I
Foundations of Lie Theory Lie Transformation Groups
Inbunden, Engelska, 1993
1 064 kr
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The book by Gorbatsevich, Onishchik and Vinberg is the firstin a series of volumes devoted to the theory of Lie groupsand Lie algebras.The first part of the book deals with the foundations of thetheory based on the classical global approach of Chevalleyfollowed by an exposition of the alternative approach viathe universal algebra and the Campbell-Hausdorff formula. Italso contains a survey of certain generalizations of Liegroups.The second more advanced part treats the topic of Lietransformation groups covering e.g. properties of orbits andstabilizers, homogeneous fibre bundles, Frobenius duality,groups ofautomorphisms of geometric structures, Liealgebras of vector fields and theexistence of slices. Thework of the last decades including the most recentresearch results is covered.The book contains numerous examples and describesconnections with topology, differential geometry, analysisand applications. It will be of great interest to graduatestudents and researchers in mathematics and theoreticalphysics.
Lie Groups and Lie Algebras II
Discrete Subgroups of Lie Groups and Cohomologies of Lie Groups and Lie Algebras
Inbunden, Engelska, 1999
1 064 kr
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The first part of this book on Discrete Subgroups of Lie Groups is written by E.B. Vinberg, V.V. Gorbatsevich, and O.V. Shvartsman. Various types of discrete subgroups of Lie groups arise in the theory of functions of complex variables, arithmetic, geometry, and crystallography. Since the foundation of their general theory in the 50-60s of this century, considerable and in many respects exhaustive results were obtained. This development is reflected in this survey. Both semisimple and general Lie groups are considered. Part II on Cohomologies of Lie Groups and Algebras is written by B.L. Feigin and D. B.Fuchs. It contains different definitions of cohomologies of Lie groups and (both finite-dimensional and some infinite-dimensional) Lie algebras, the main methods of their calculation, and the results of these calculations. The book can be useful as a reference and research guide to graduate students and researchers in different areas of mathematics and theoretical physics.
1 473 kr
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This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian goemetry and group theory. The result is a book which has no rival in the literature. Part I contains the classification of motions in spaces of constant curvature and non-traditional topics like the theory of acute-angled polyhedra and methods for computing volumes of non-Euclidean polyhedra. Part II includes the theory of cristallographic, Fuchsian, and Kleinian groups and an exposition of Thurston's theory of deformations. The greater part of the book is accessible to first-year students in mathematics. At the same time the book includes very recent results which will be of interest to researchers in this field.
Del 20 - Encyclopaedia of Mathematical Sciences
Lie Groups and Lie Algebras I
Foundations of Lie Theory Lie Transformation Groups
Häftad, Engelska, 1996
1 064 kr
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From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ...On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter"...Both parts are very nicely written and can be strongly recommended. " European Mathematical Society
Del 21 - Encyclopaedia of Mathematical Sciences
Lie Groups and Lie Algebras II
Discrete Subgroups of Lie Groups and Cohomologies of Lie Groups and Lie Algebras
Häftad, Engelska, 2010
1 064 kr
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The first part of this book on Discrete Subgroups of Lie Groups is written by E.B. It contains different definitions of cohomologies of Lie groups and (both finite-dimensional and some infinite-dimensional) Lie algebras, the main methods of their calculation, and the results of these calculations.
Del 29 - Encyclopaedia of Mathematical Sciences
Geometry II
Spaces of Constant Curvature
Häftad, Engelska, 2011
1 473 kr
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Spaces of constant curvature, i.e. Euclidean space, the sphere, and Loba chevskij space, occupy a special place in geometry. They are most accessible to our geometric intuition, making it possible to develop elementary geometry in a way very similar to that used to create the geometry we learned at school. However, since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space, the original source of our geometric intuition. Euclidean geometry has for a long time been deeply rooted in the human mind. The same is true of spherical geometry, since a sphere can naturally be embedded into a Euclidean space. Lobachevskij geometry, which in the first fifty years after its discovery had been regarded only as a logically feasible by-product appearing in the investigation of the foundations of geometry, has even now, despite the fact that it has found its use in numerous applications, preserved a kind of exotic and even romantic element. This may probably be explained by the permanent cultural and historical impact which the proof of the independence of the Fifth Postulate had on human thought.