论文标题
关于几何学的奇数参数
On odd parameters in geometry
论文作者
论文摘要
1）1976年，研究简单的有限维复合物是Superalgebras，J.〜Bernstein和I，以及独立的M.〜Duflo，观察到某些无差异的矢量性lie superalgebras具有奇数参数的变形，并推测了其他简单的超级大管没有这样的变形（未公开）。在这里，我证明了这个猜想，并概述了简单的有限维复合物的已知分类超级级别，它们的演示，实现以及（非常粗略地）与简单的谎言（超级）代数（超级）代数在积极特征的领域上。 2）任何是表格的环形空间（一种歧管$ m $，矢量捆绑包上$ m $ $ m $）的截面称为拆分的任何超人。 Gawȩdzki（1977）和Batchelor（1979）证明了每个光滑的超人群都被拆分了。 1982年，绿色和帕拉莫多夫（P. Green）和帕拉莫多夫（Palamodov）表明，一个复杂的分析超曼佛可能不是分类的，即对分裂的超曼膜而不是差异。到目前为止，研究人员大部分考虑了分裂性的障碍。这导致他们得出的结论是，任何超数$ m | 1 $的超级势力均已分开。我将证明有超数$ m | 1 $的非分类超曼佛。例如，某些$ 1 | 1 $维度超级线，其分裂性的障碍物对应于奇数参数。
1) In 1976, looking at simple finite-dimensional complex Lie superalgebras, J.~Bernstein and I, and independently M.~Duflo, observed that certain divergence-free vectorial Lie superalgebras have deformations with odd parameters and conjectured that other simple Lie superalgebras have no such deformations (unpublished). Here, I prove this conjecture and overview the known classification of simple finite-dimensional complex Lie superalgebras, their presentations, realizations, and (very sketchily) relations with simple Lie (super)algebras over fields of positive characteristic. 2) Any supermanifold which is a ringed space of the form (a manifold $M$, the sheaf of sections of the exterior algebra of a vector bundle over $M$) is called split. Gawȩdzki (1977) and Batchelor (1979) proved that every smooth supermanifolds is split. In 1982, P. Green and Palamodov showed that a~complex-analytic supermanifold can be non-split, i.e., not diffeomorphic to a split supermanifold. So far, researchers considered, mostly, even obstructions to splitness. This lead them to the conclusion that any supermanifolds of superdimension $m|1$ is split. I'll show that there are non-split supermanifolds of superdimension $m|1$; for example, certain $1|1$-dimensional superstrings, the obstructions to their splitness correspond to odd parameters.
