Local Symplectic Algebra of Quasi-homogeneous Curves

Local Symplectic Algebra and Simple Symplectic Singularities of Curves

We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold in [A1]. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a quasihomogeneous curve is a finite dimensional vector space. We also show that the action of local diffe...

Symplectic singularities of varieties: The method of algebraic restrictions

We study germs of singular varieties in a symplectic space. In [A1], V. Arnol’d discovered so called ‘‘ghost’’ symplectic invariants which are induced purely by singularity. We introduce algebraic restrictions of di¤erential forms to singular varieties and show that this ghost is exactly the invariants of the algebraic restriction of the symplectic form. This follows from our generalization of ...

2 00 6 Algebraic computation of some intersection D - modules

Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this paper we give an algebraic description in terms of E of the regular holonomic DX-module whose de Rham complex is the intersection complex associated with L. As an application, we pe...

Convolution and Homogeneous Spaces

g-QUASI-FROBENIUS LIE ALGEBRAS

A Lie version of Turaev’s G-Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a g-quasi-Frobenius Lie algebra for g a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra (q, β) together with a left g-module structure which acts on q via derivations and for which β is g-inva...