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 ∗

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 ∗

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) = P ol(T * M) of all polynomial functions on T * M, the symbols of the operators in D(M). It turns out that, in terms ...

ar X iv : m at h / 05 01 55 6 v 1 [ m at h . D G ] 3 1 Ja n 20 05 Geometric Algebras

This is the first paper in a series of three where we develope a systematic approach to the geometric algebras of multivectors and ex-tensors. The series is followed by another one where those algebraic concepts are used in a novel presentation of the differential geometry of (smooth) manifolds of arbitrary global topology. The key calcu-lational tool in our program is the euclidean geometrical...

ar X iv : 0 81 2 . 04 22 v 2 [ m at h . D G ] 1 6 Ja n 20 09 On the ∂ - and ∂̄ - Operators of a Generalized Complex Structure ∗

In this note, we prove that the ∂and ∂̄-operators introduced by Gualtieri for a generalized complex structure coincide with the d̆∗and ∂̆-operators introduced by Alekseev-Xu for Evens-Lu-Weinstein modules of a Lie bialgebroid.

ar X iv : m at h / 05 01 25 7 v 1 [ m at h . C A ] 1 7 Ja n 20 05 FACTORIZATION OF SYMMETRIC POLYNOMIALS

We construct linear operators factorizing the three bases of symmetric polynomials: monomial symmetric functions mλ(x), elementary symmetric polynomials Eλ(x), and Schur functions sλ(x), into products of univariate polynomials.

ar X iv : h ep - t h / 03 01 12 7 v 1 1 7 Ja n 20 03 Supersymmetry in Spaces of Constant Curvature