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...
Gespeichert in:
| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2023
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| In: |
Journal of Lie theory
Year: 2023, Jahrgang: 33, Heft: 2, Pages: 567-608 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://www.heldermann.de/JLT/JLT33/JLT332/jlt33024.htm
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| Verfasserangaben: | C.A. Cremonini, P.A. Grassi, S. Noja |
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| 245 | 1 | 0 | |a Cohomology of Lie superalgebras |b forms, integral forms and coset superspaces |c C.A. Cremonini, P.A. Grassi, S. Noja |
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| 520 | |a 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. | ||
| 650 | 4 | |a ALGEBRA | |
| 650 | 4 | |a Chevalley-Eilenb erg cohomology | |
| 650 | 4 | |a coset superspace | |
| 650 | 4 | |a differential forms | |
| 650 | 4 | |a GEOMETRY | |
| 650 | 4 | |a integral forms | |
| 650 | 4 | |a Lie superalgebras | |
| 650 | 4 | |a RHAM | |
| 650 | 4 | |a SUPERMANIFOLDS | |
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