We investigate a new cohomology of Lie superalgebras, which may be compared to a de Rham cohomology of Lie supergroups involving both differential and integral forms. It is defined by a BRST complex of Lie superalgebra modules, which is formulated in terms of a Weyl superalgebra and incorporates inequivalent representations of the bosonic Weyl subalgebra. The new cohomology includes the standard Lie superalgebra cohomology as a special case. Examples of new cohomology groups are computed.

中文翻译：

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李超代数的混合上同调

我们研究了李超代数的新上同调，它可以与李超群的 de Rham 上同调相比较，该上同调包括微分形式和积分形式。它由李超代数模的 BRST 复形定义，该复形根据外尔超代数公式化，并结合了玻色外尔子代数的不等价表示。新的上同调包括标准李超代数上同调作为一个特例。计算新的上同调群的例子。