Cohomology of orthosymplectic contactomorphisms acting on λ-densities on the 1|n-supercircle
DOI:
https://doi.org/10.17398/Keywords:
Group of contactomorphisms, euclidean structures, orthosymplectic superalgebra, supermanifoldsAbstract
We study the standard contact structure on the supercircle, S 1|n , and the associated supergroups of contactomorphisms E(1|n) and OPs(n|2) corresponding to Euclidean and projective geometries. In this work, we begin by computing the cohomology group of the orthosymplectic Lie group PC(n|2), taking values in the space of tensor densities, Fnλ . Second, we determine the s(2|n)-relative cohomology spaces H1diff (osp(n|2), s(2|n); Fnλ ) with H1diff indicating that only differential cochains are considered; meaning that only cochains given by differential operators are taken into account. We also explicitly determine the 1-cocycles generating these cohomology spaces.
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