Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces
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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Cite
@article{arxiv.2012.05246,
title = {Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces},
author = {R. Catenacci and C. A. Cremonini and P. A. Grassi and S. Noja},
journal= {arXiv preprint arXiv:2012.05246},
year = {2020}
}
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