论文标题
在由$ \Overlineμ，\ edline {\ partial}，\ partial，μ$生成的代数上
On the algebra generated by $\overlineμ, \overline{\partial}, \partial, μ$
论文作者
论文摘要
在本说明中，我们确定由差分运算符$ \Overlineμ，\ Overline {\ partial}，\ partial，μ$生成的关联代数的结构，这些结构是对复杂值的差异形式作用于几乎复杂的歧管的复杂差分形式。这是通过证明它是由这些运算符产生的分级谎言代数的通用代数并确定相应分级的LIE代数的结构来完成的。然后，我们根据其规范的内部差异$ [d， - ] $及其在其所有内部差异方面的共同差异$ [d， - ] $及其共同体学确定了该分级谎言代数的共同体学。
In this note, we determine the structure of the associative algebra generated by the differential operators $\overlineμ, \overline{\partial}, \partial, μ$ that act on complex-valued differential forms of almost complex manifolds. This is done by showing it is the universal enveloping algebra of the graded Lie algebra generated by these operators and determining the structure of the corresponding graded Lie algebra. We then determine the cohomology of this graded Lie algebra with respect to its canonical inner differential $[d,-]$, as well as its cohomology with respect to all its inner differentials.
