Correction to: Differential Geometry and Lie Groups

Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.

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Differential geometry, Lie groups and symmetric spaces over general base fields and rings

Memoirs of the American Mathematical Society ◽

10.1090/memo/0900 ◽

2008 ◽

Vol 192 (900) ◽

pp. 0-0 ◽

Cited By ~ 8

Author(s):

Wolfgang Bertram

Keyword(s):

Differential Geometry ◽

Lie Groups ◽

Symmetric Spaces ◽

General Base

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Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras

Georgian Mathematical Journal ◽

10.1515/gmj.1995.425 ◽

1995 ◽

Vol 2 (4) ◽

pp. 425-444

Author(s):

Jean Marion ◽

Thierry Robart

Keyword(s):

Differential Geometry ◽

Lie Groups ◽

Wide Class ◽

Fundamental Theorem ◽

Banach Algebras ◽

Inverse Limits ◽

Topological Algebras ◽

Infinite Dimensional ◽

Dimensional Version ◽

Invertible Elements

Abstract We consider a wide class of unital involutive topological algebras provided with a C*-norm and which are inverse limits of sequences of unital involutive Banach algebras; these algebras are taking a prominent position in noncommutative differential geometry, where they are often called unital smooth algebras. In this paper we prove that the group of invertible elements of such a unital solution smooth algebra and the subgroup of its unitary elements are regular analytic Fréchet–Lie groups of Campbell–Baker–Hausdorff type and fulfill a nice infinite-dimensional version of Lie's second fundamental theorem.

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Problems on rigidity of group actions and cocycles

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700003084 ◽

1985 ◽

Vol 5 (3) ◽

pp. 473-484 ◽

Cited By ~ 8

Author(s):

S. Hurder

Keyword(s):

Differential Geometry ◽

Lie Groups ◽

Ergodic Theory ◽

Positive Curvature ◽

Group Actions ◽

Geodesic Flows ◽

Mathematical Sciences ◽

Research Institute

AbstractA conference on the interaction of ergodic theory, differential geometry and the theory of Lie Groups was held at the Mathematical Sciences Research Institute from May 24 to June 1, 1984. This is a report of the problem session organized by A. Katok and R. Zimmer and held on May 25, 1984 dealing with the topics in the title. Another problem session was centred on the rigidity of manifolds of non-positive curvature and related topics concerning their geodesic flows. This is reported on by K. Burns and A. Karok separately [2].

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