超Schr?dinger代数■(1/1)的上同调

Cohomology of the Super Schr?dinger Algebra ■(1/1)

本文具体计算了系数在超Schr?dinger代数■(1/1)的平凡模和有限维不可约模中的第一阶上同调群与第二阶上同调群,并给出了系数在通用包络代数U(■(1/1))中■(1/1)的第一阶与第二阶上同调群的维数是无限维的.

We explicitly compute the first and second cohomology groups of the Super Schrodinger algebra■(1/1) with coefficients in the trivial module and the finitedimentional irreducible modules. We also show that the first and second cohomology groups of■(1/1) with coefficients in the universal enveloping algebras U(■(1/1))(under the adjoint action) are infinite dimensional.