On isometry groups of pseudo-Riemannian compact Lie groups

ISOMETRY GROUPS OF k-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

We study the isometry groups of a family of complete p + 2curvature homogeneous pseudo-Riemannian metrics on R which have neutral signature (3 + 2p, 3 + 2p), and which are 0-curvature modeled on an indecomposible symmetric space.

Compact Metrizable Groups Are Isometry Groups of Compact Metric Spaces

This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.

-bounds for Pseudo-differential Operators on Compact Lie Groups

Given a compact Lie group G, in this paper we establish L p-bounds for pseudo-differential operators in L p(G). The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space G× Ĝ, where Ĝ is the unitary dual of G. We obtain two different types of L p bounds: first for finite regularity symbols and second for smooth symbols. The c...

Probability on Compact Lie Groups

Sub-Riemannian structures on 3D Lie groups

We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A(R)× S, where A(R) denotes the group of orientation preserving affine maps on the real line.