Real semisimple Lie groups and balanced metrics

Equivariant derived category and representation of real semisimple Lie groups

Representations of Semisimple Lie Groups

Let G be a Lie group and § a Banach space. A representation n of G on § is a mapping which assigns to every element x in G a bounded linear operator n(x) on § such that the following two conditions are fulfilled: (1) 7t(xy) = n(x) 7i(y) (x, y e G),n(l) = / and (2) the mapping (x, tp) ->uz(x)y) of G x § into § is continuous. (Here 1 is the unit element of G and I is the unit operator,) In partic...

Representations of Semisimple Lie Groups

Fifty years ago, at the International Congress in Bologna, Hermann Weyl gave a report on representations of compact groups and, in particular, of compact Lie groups. Most of the important results had just been proved by him and by others, and at the time of his lecture, in 1928, the representation theory of compact Lie groups had become a very appealing subject. To a large extent, Weyl's theory...

Realizations of real semisimple low-dimensional Lie algebras Realizations of real semisimple low-dimensional Lie algebras

A complete set of inequivalent realizations of threeand four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained. Representations of Lie algebras by vector fields are widely applicable e.g. in integrating of ordinary differential equations, group classification of partial differential equations, the theory of differential...

Livšic’s theorem for semisimple Lie groups

In this paper we show that strong generalizations of the measurable Livšic theorem for cocycles taking values in connected non-compact linear semisimple Lie groups, a canonical example being SL(2,R), can be deduced from an elegant approach of Brin and Pesin to the dynamics of partially hyperbolic systems.