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Applications of Lie groups to differential equations by Peter J. Olver

Applications of Lie groups to differential equations Peter J. Olver ebook
Publisher: Springer-Verlag
Page: 640
ISBN: 0387962506, 9780387962504
Format: djvu

There is a refinement of smooth ∞ -groupoids to synthetic differential ∞-groupoids. DifferentialGeometry is a Maple software package which symbolically performs fun- damental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations. The goal of the lectures was to present some of the recent uses of nilpotent Lie groups in the representation theory of semi-simple Lie groups, complex analysis, and partial differential equations. The preferred research area lies in nonlinear partial differential equations related to geometry and mathematical physics. Literature on Lie groups and Lie algebras, one uses (i), in which case the existence and basic properties of the exponential map can be provided by the Picard existence theorem from the theory of ordinary differential equations. To define the Lie algebra of a Lie group, we must first quickly recall some basic notions from differential geometry associated to smooth manifolds (which are not necessarily embedded in some larger Euclidean space, but instead exist .. For standard references on differential geometry and Lie groupoids see there. The successful applicant is expected to participate in the supervision of PhD students and will have The University of Potsdam and the Max Planck Society are committed to support the appointment of severely handicapped people, applications are explicitly encouraged. Areas including commutative normed rings and functional analysis, representation theory of Lie groups and Lie algebras, generalized functions, mathematical physics, partial differential equations, and theoretical biology. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. See SynthDiff∞Grpd for more . Olver: Applications of Lie Groups to Differential Equations (Springer, New York, 1986).