Tate–Shafarevich groups and algebras

Hopf algebras for ternary algebras and groups

We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters ...

Operator Algebras, Free Groups and Other Groups

The operator algebras associated to non commutative free groups have received a lot of attention, by F.J. Murray and J. von Neumann and by later workers. We review some properties of these algebras, both for free groups and for other groups such as lattices in Lie groups and Gromov hyperbolic groups. Our guideline is the following list of results for the free group Fn over n ≥ 2 generators. (1)...

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

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