In this paper we consider the so-called twisted Heisenberg superalgebras over the complex number field, which are defined by adding derivations to Heisenberg superalgebras. By introducing the concept of blocks of type I, II and III for a Lie superalgebra, we classify the fine gradings up to equivalence on the twisted Heisenberg superalgebras and determine the Weyl groups of those gradings.

中文翻译：

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扭曲的海森堡李超代数的精细分级及其外尔群

在本文中，我们考虑了复数域上所谓的扭曲海森堡超代数，这些超代数是通过向海森堡超代数添加导数来定义的。通过为李超代数引入类型 I、II 和 III 的块的概念，我们对扭曲的 Heisenberg 超代数上的等价的精细分级进行分类，并确定这些分级的 Weyl 群。