Lie Atoms and their deformation theory
Algebraic Geometry
2007-06-13 v7
Abstract
A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of deformations with respect to one algebra together with a trivialization with respect to the other. Such deformations occur commonly in Algebraic Geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi-Bernoulli cohomology, which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by certain Kodaira-Spencer data.(minor corrections Feb'06/May'07; paper is to appear in GAFA)
Cite
@article{arxiv.math/0412204,
title = {Lie Atoms and their deformation theory},
author = {Ziv Ran},
journal= {arXiv preprint arXiv:math/0412204},
year = {2007}
}