论文标题
Golod-Shafarevich-Vinberg类型定理和潜在代数的有限条件
Golod-Shafarevich-Vinberg type theorems and finiteness conditions for potential algebras
论文作者
论文摘要
我们通过提供Golog-Shafarevich-Vinberg定理的潜在案例的类似物来获得Hilbert系列的Jacobi代数及其完成的较低估计。我们特别处理非均匀情况。该估计值允许回答Wemyss-Donovan-Brown对非交通性奇异性和变形理论的工作中产生的问题数。特别是，我们证明了潜在的代数或其完成可能是有限维度或线性增长的唯一情况，是两个变量和潜力具有三级术语的情况。
We obtain a lower estimate for the Hilbert series of Jacobi algebras and their completions by providing analogue of the Golog-Shafarevich-Vinberg theorem for potential case. We especially treat non-homogeneous situation. This estimate allows to answer number of questions arising in the work of Wemyss-Donovan-Brown on noncommutative singularities and deformation theory. In particular, we prove that the only case when a potential algebra or its completion could be finite dimensional or of linear growth, is the case of two variables and potential having terms of degree three.
