Mixed Cohomology Of Low-dimensional Nilpotent Lie Superalgebras

In the study of Lie algebras and Lie superalgebras,the cohomology problem is always an important research topic.Nilpotent Lie superalgebras as a special Lie superalgebra,it is of great significance to study its cohomology.In this article,we study mixed cohomology of Lie superalgebras defined by BRST complexes.Firstly,we establish cochain which is the tensor product of mixed Fock spaces and corresponding Lie superalgebra modules,introduce differential-integral operators to defined the mixed cohomology of Lie superalgebras.Secondly,according to the classification of low-dimensional nilpotent Lie superalgebras over complex fields,the coefficients of low-dimensional nilpotent Lie superalgebras over complex fields are characterized by the mixed cohomology of trivial modules.