Trace map, Cayley transform and LS category of Lie groups

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

Equivariant derived category and representation of real semisimple Lie groups

Structure of Symplectic Lie groups and momentum map

We describe the structure of the Lie groups endowed with a leftinvariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This description is particularly nice if the group is Hamiltonian, that is, if the left canonical action of the group on itself is Hamiltonian. The principal tool used...

Lie Algebras and Lie Brackets of Lie Groups–matrix Groups

The goal of this paper is to study Lie groups, specifically matrix groups. We will begin by introducing two examples: GLn(R) and SLn(R). Then in each section we will prove basic results about our two examples and then generalize these results to general matrix groups.

Martingale Transform and Lévy Processes on Lie Groups

This paper constructs a class of martingale transforms based on Lévy processes on Lie groups. From these, a natural class of bounded linear operators on the Lp-spaces of the group (with respect to Haar measure) for 1 < p < ∞, are derived. On compact groups these operators yield Fourier multipliers (in the Peter-Weyl sense) which include the second order Riesz transforms, imaginary powers of the...