Download or read book Lie Derivations on Rings of Differential Operators written by Myungsuk Chung and published by . This book was released on 1995 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rings of Differential Operators on Classical Rings of Invariants written by Thierry Levasseur and published by American Mathematical Soc.. This book was released on 1989 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: "September 1989, Volume 81, number 412 (third of 6 numbers)."
Download or read book Rings of Differential Operators written by Jan-Erik Björk and published by North-Holland. This book was released on 1979 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Invariant Differential Operators and the Cohomology of Lie Algebra Sheaves written by Franz W. Kamber and published by American Mathematical Soc.. This book was released on 1971 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a Lie algebra sheaf L of derivations of a sheaf of rings O on a space X global cohomology groups and local cohomology sheaves are introduced and analyzed. Global and local splitting obstructions for extensions of modules over a Lie algebra sheaf are studied. In the applications considered, L is a Lie algebra sheaf of vector fields on a manifold M, O the structure sheaf of M. For vector bundles E, F on M on which L acts, the existence of invariant differential operators D: E→F whose symbols are preassigned equivariant maps is discussed in terms of these splitting obstructions. Lie algebra sheaves defined by Lie group actions are considered. This theory is applied in particular to the case of a transitive L. The splitting obstructions for extensions of modules over a transitive Lie algebra sheaf are analyzed in detail. The results are then applied to the problem of the existence of invariant connections on locally homogeneous spaces. The obstruction is computed in some examples.
Download or read book Algorithmic Lie Theory for Solving Ordinary Differential Equations written by Fritz Schwarz and published by CRC Press. This book was released on 2007-10-02 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Download or read book Notes on Crystalline Cohomology MN 21 written by Pierre Berthelot and published by . This book was released on 2015-02-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Prime Ideals in Differential Operator Rings and Crossed Products written by William Chin and published by . This book was released on 1985 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Theory of Locally Nilpotent Derivations written by Gene Freudenburg and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings. The book also includes a wealth of pexamples and open problems.
Download or read book Algebraic Theory of Locally Nilpotent Derivations written by Gene Freudenburg and published by Springer. This book was released on 2017-09-08 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Download or read book Galois Theory of Linear Differential Equations written by Marius van der Put and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Download or read book A Study of Derivations in Rings written by Radwan Mohammed Abdullah Al-Omary and published by LAP Lambert Academic Publishing. This book was released on 2011-09 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: New book on Derivations in rings. The theory of derivations and automorphisms plays an important role not only in ring theory, but also in functional analysis, linear differential equations concerning the question of innerness and outerness, for instance, the classical Noether-Skolem theorem yields the solution of the problem for finite dimensional central simple algebras. At places, examples are provided to justify the conditions imposed on the hypothesis of various results. Also suitable remarks are given sometime to explain the theory and sometime to conjecture the possible extensions of the results. In the end, an exhaustive references of the existing material related to the subject matter of our thesis is included which may serve as source material for those, interested in the domain of our research.
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Download or read book Rings with Generalized Identities written by Konstant I. Beidar and published by CRC Press. This book was released on 1995-11-17 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Discusses the latest results concerning the area of noncommutative ring theory known as the theory of generalized identities (GIs)--detailing Kharchenko's results on GIs in prime rings, Chuang's extension to antiautomorphisms, and the use of the Beidar-Mikhalev theory of orthogonal completion in the semiprime case. Provides novel proofs of existing results."
Download or read book Foundations of Arithmetic Differential Geometry written by Alexandru Buium and published by American Mathematical Soc.. This book was released on 2017-06-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Download or read book Lie Algebras of Bounded Operators written by Daniel Beltita and published by Birkhäuser. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.
Download or read book Introduction to Finite and Infinite Dimensional Lie Super algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. - Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory - Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities - Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras - Focuses on Kac-Moody algebras
Download or read book Lie Algebras of Differential Operators and D modules written by Dmitry Donin and published by . This book was released on 2008 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In our thesis we study the algebras of differential operators in algebraic and geometric terms. We consider two problems in which the algebras of differential operators naturally arise. The first one deals with the algebraic structure of differential and pseudodifferential operators. We define the Krichever-Novikov type Lie algebras of differential operators and pseudodifferential symbols on Riemann surfaces, along with their outer derivations and central extensions. We show that the corresponding algebras of meromorphic differential operators and pseudodifferential symbols have many invariant traces and central extensions, given by the logarithms of meromorphic vector fields. We describe which of these extensions survive after passing to the algebras of operators and symbols holomorphic away from several fixed points. We also describe the associated Manin triples, emphasizing the similarities and differences with the case of smooth symbols on the circle.The second problem is related to the geometry of differential operators and its connection with representations of semi-simple Lie algebras. We show that the semiregular module, naturally associated with a Z -graded semi-simple complex Lie algebra g , can be realized in geometric terms, using the Brion's construction of degeneration of the diagonal in the square of the flag variety of g . Namely, we consider the Beilinson-Bernstein localization of the semiregular module and show that it is isomorphic to the D-module obtained by applying the Emerton-Nadler-Vilonen geometric Jacquet functor to the D-module of distributions on the square of the flag variety with support on the diagonal.
