Lie Atoms and Their Deformations
Lie Atoms and Their Deformations
复制标题
谎言原子及其变形
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Z. Ran
中科院分区：
文献类型：
--
作者：
Z. Ran
李原子本质上是一对李代数，它的形变理论是相对于第一代数的形变理论，具有相对于第二代数的平凡。这种变形通常发生在代数几何中，例如作为固定环境变化的子簇的变形。在这里，我们研究了与李原子有关的一些基本概念，特别是它们的形变理论，特别是普适形变。我们引入了产生形变环的Jacobi-Bernoulli上同调，并证明了在适当的假设下，无限小的变形可以用某些Kodaira-Spencer数据来分类。
Abstract.A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. 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.