Nagel and colleagues study algebras of singular integral operators on Rn and nilpotent Lie groups
that arise when considering the composition of Calder n-Zygmund operators with different homogeneties, such as operators occurring in sub-elliptic problems and these arising in elliptic problems.
Berg, "An intrinsic robust PID controller on Lie groups
," in Proceedings of the 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, pp.
Olver, Applications of Lie Groups
to Differential Equations, vol.
Such groups are called Lie groups
and are invertible point transformations of both the dependent and independent variables of the differential equations.
 W Marzantowicz, An almost classification of compact Lie groups
with Borsuk-Ulam properties, Pacific J.
Kobayashi, Discontinuous groups acting on homogeneous spaces of reductive type, in Representation theory of Lie groups
and Lie algebras (Fuji-Kawaguchiko, 1990), 59 75, World Sci.
With this Marie-Curie fellowship, I pick up the two challenges of construction and classification, especially focussing on Connes~ famous rigidity conjecture for lattices in Lie groups
as well as type III von Neumann algebras, using two entirely new approaches.
Recall that a [S.sup.1]-central extension of a Lie group
G is an extension [??] of G which fits in the short exact sequence of Lie groups
The first edition, published in 1998, was intended as a self-contained work with a focus on structure theory rather than on representation theory or abstract harmonic analysis, although those topics were addressed; also included was such material as an introduction to linear Lie groups
, abstract abelian groups, and category theory.
However, the Riemannian mean on the special Euclidean group SE(n) and the unipotent matrix group UP(n),which are the noncompact matrix Lie groups
, has not been well studied.
The method of Lie groups
applied to differential equations gives an explicit and algorithmic way to compute invariant solutions for a wide range of equations.
Flows on homogenous spaces of algebraic groups or Lie groups
, and dynamics on moduli spaces of abelian or quadratic differentials on surfaces are distinct but related areas of research with some common roots and features.