Geodesic
Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces
Journal of Lie theory, Tome 33 (2023) no. 2, pp. 567-608
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We study Chevalley-Eilenberg cohomology of physically relevant Lie superalgebras related to supersymmetric theories, providing explicit expressions for their cocycles in terms of their Maurer-Cartan forms. We include integral forms in the picture by defining the notions of constant densities and integral forms related to a Lie superalgebra. We develop a suitable generalization of Chevalley-Eilenberg cohomology extended to integral forms and we prove that it is isomorphic via a Poincaré duality-type pairing to the ordinary Chevalley-Eilenberg cohomology of the Lie superalgebra. Next, we study equivariant Chevalley-Eilenberg cohomology for coset superspaces, which play a crucial role in supergravity and superstring models. Again, we treat explicitly several examples, providing cocycles' expressions and revealing a characteristic infinite-dimensional cohomology.
Classification : 17B56, 17B81
Mots-clés : Lie superalgebras, Chevalley-Eilenberg cohomology, coset superspace, differential forms, integral forms 
@article{JLT_2023_33_2_JLT_2023_33_2_a5,
     author = {C. A. Cremonini and P. A. Grassi and S. Noja},
     title = {Cohomology of {Lie} {Superalgebras:} {Forms,} {Integral} {Forms} and {Coset} {Superspaces}},
     journal = {Journal of Lie theory},
     pages = {567--608},
     year = {2023},
     volume = {33},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2023_33_2_JLT_2023_33_2_a5/}
}
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C. A. Cremonini; P. A. Grassi; S. Noja. Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces. Journal of Lie theory, Tome 33 (2023) no. 2, pp. 567-608. http://geodesic.mathdoc.fr/item/JLT_2023_33_2_JLT_2023_33_2_a5/