AI 中文总结
该研究基于已有代数分类，确定低维复左对称代数与左对称超代数同构类的退化关系，明确3维左对称代数簇的维数、不可约分支数及刚性分支，还给出对应维数左对称超代数的不可约分支、维数与刚性超代数。
AI 中文摘要
我们研究低维复左对称代数与左对称超代数的几何分类。基于Bai和Zhang对3维左对称代数、2维和3维左对称超代数的代数分类，我们确定其同构类间的所有退化与非退化关系。我们证明3维左对称代数的簇维数为10，分解为31个不可约分支，其中10个是刚性的。对于左对称超代数，我们描述其不可约分支，确定其维数，并在(1,1)、(1,2)和(2,1)维数的簇中识别出刚性超代数。
英文摘要
We investigate the geometric classification of complex left-symmetric algebras and left-symmetric superalgebras in low dimensions. Building on the algebraic classifications of Bai and Zhang for 3-dimensional left-symmetric algebras and for 2- and 3-dimensional left-symmetric superalgebras, we determine all degenerations and non-degenerations among their isomorphism classes. We prove that the variety of 3-dimensional left-symmetric algebras has dimension 10 and decomposes into 31 irreducible components, ten of which are rigid. For left-symmetric superalgebras, we describe the irreducible components, determine their dimensions, and identify the rigid superalgebras in the varieties of dimensions (1,1), (1,2), and (2,1).
