When unit groups of continuous inverse algebras are regular Lie groups
It is a basic fact in infinite-dimensional Lie theory that the unit group of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group is regular in Milnor’s sense. Notably, is regular if A is Mackey-complete and locally m-convex.
Wiener functionals on spaces of Lie algebra valued 1-currents, and unitary representations of currents groups.
Witt algebra and the curvature of the Heisenberg group
The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.