Cohomology of Lie superalgebras: forms, integral forms and coset superspaces
We study Chevalley-Eilenb erg 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 in...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2023
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| In: |
Journal of Lie theory
Year: 2023, Volume: 33, Issue: 2, Pages: 567-608 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://www.heldermann.de/JLT/JLT33/JLT332/jlt33024.htm
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| Author Notes: | C.A. Cremonini, P.A. Grassi, S. Noja |
| Summary: | We study Chevalley-Eilenb erg 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-Eilenb erg cohomology extended to integral forms and we prove that it is isomorphic via a Poincare duality-type pairing to the ordinary Chevalley-Eilenb erg cohomology of the Lie superalgebra. Next, we study equivariant Chevalley-Eilenb erg 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. |
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| Item Description: | Gesehen am 25.07.2023 |
| Physical Description: | Online Resource |