ar X iv : m at h / 03 12 16 2 v 1 [ m at h . D G ] 8 D ec 2 00 3 Derivations of the Lie algebras of differential operators ∗

ar X iv : m at h / 03 12 16 2 v 2 [ m at h . D G ] 1 7 Ja n 20 05 Derivations of the Lie algebras of differential operators ∗

This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M , of its Lie subalgebra D 1 (M) of all linear first-order differential operators of M , and of the Poisson algebra S(M) = Pol(T * M) of all polynomial functions on T * M, the symbols of the operators in D(M). It turns out that, in terms o...

ar X iv : m at h / 04 12 16 9 v 1 [ m at h . D G ] 8 D ec 2 00 4 TABLEAUX OVER LIE ALGEBRAS , INTEGRABLE SYSTEMS , AND CLASSICAL SURFACE THEORY

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, projective minimal surfaces, and other classical soliton surfaces. Completely integrable equations suc...

ar X iv : m at h / 03 08 16 9 v 3 [ m at h . FA ] 1 1 D ec 2 00 3 Applications of operator spaces to abstract harmonic analysis

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).

ar X iv : m at h / 03 12 22 1 v 1 [ m at h . R A ] 1 1 D ec 2 00 3 three talks on noncommutative geometry

ar X iv : m at h / 06 12 11 7 v 1 [ m at h . D G ] 5 D ec 2 00 6 Nilradicals of Einstein solvmanifolds

A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less th...