2004/12/10 by Ziv Ran, Ran, Ziv
Chemistry · Mathematics · #14d15 #32g10 #Algebraic Geometry (math.AG) #FOS: Mathematics #History and advancements in chemistry #Molecular spectroscopy and chirality #math.AG #msc:14d15 #msc:32g10
paper · pdf · doi:10.48550/arxiv.math/0412204
openalex publication_date 2004/12/10 · arxiv created 2007/05/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)