Finiteness conditions in soluble groups and Lie algebras

Homological finiteness conditions for groups, monoids and algebras

Recently several different homological finitenes conditions have been introduced for monoids. I will survey the interplay between these notions. It is, in fact, more natural (and more illuminating) to work in the wider context of associative algebras.

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...

Lie Groups and Lie Algebras in Robotics

In this lecture the group of rigid body motions is introduced via its representation on standard three dimensional Euclidian space. The relevance for robotics is that the links of a robot are usually modelled as rigid bodies. Moreover the payload of a robot is also usually a rigid body and hence much of robotics is concerned with understanding rigid transformations and sequences of these transf...