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arXiv · 2012.05246

Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces

R. Catenacci·C. A. Cremonini·P. A. Grassi·S. Noja
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Abstract

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 then include integral forms in the picture by defining a notion of 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 to the ordinary Chevalley-Eilenberg cohomology of the Lie superalgebra. Next we study equivariant Chevalley-Eilenberg cohomology for coset superspaces, which plays a crucial role in supergravity and superstring models. Again, we treat explicitly several examples, providing cocycles' expressions and revealing a characteristic infinite dimensional cohomology.

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R. Catenacci, C. A. Cremonini, P. A. Grassi, S. Noja. 2020-12-09. Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces. https://arxiv.org/abs/2012.05246

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