论文标题
与括号和桁架相关的收缩代数和前lie代数的分类
Classification of contraction algebras and pre-Lie algebras associated to braces and trusses
论文作者
论文摘要
我们开发用于分类代数分类的工具，并将其应用于分类方面的问题，直至同构为8和9尺寸代数，对应于3倍FLOPS。我们证明，尺寸8的同构收缩代数只有一个，以及两个维度9的代数。在本文的第二部分中，我们表明，与适当的降级理想过滤相关的分级结构与支撑和桁架相关。
We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism contraction algebra of dimension 8, and two algebras of dimension 9. The formulae for the dimension of algebra, depending on the type of the potential are obtained. In the second part of the paper we show that associated graded structure to brace and truss with appropriate descending ideal filtration is pre-Lie.
