Differential invariant algebras of Lie pseudo-groups

Differential Invariant Algebras of Lie Pseudo–Groups

The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...

Differential Invariants for Lie Pseudo-groups

Lie pseudo-groups, roughly speaking, are the infinite-dimensional counterparts of local Lie groups of transformations. Pseudo-groups were first studied systematically at the end of the 19th century by Sophus Lie, whose great insight in the subject was to postulate the additional condition that pseudo-group transformations form the general solution to a system of partial differential equations, ...

Lie Algebras, Algebraic Groups, and Lie Groups

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...

Lie Groups and Lie Algebras

Lie Groups and Lie Algebras

A Lie group is, roughly speaking, an analytic manifold with a group structure such that the group operations are analytic. Lie groups arise in a natural way as transformation groups of geometric objects. For example, the group of all affine transformations of a connected manifold with an affine connection and the group of all isometries of a pseudo-Riemannian manifold are known to be Lie groups...