2010/11/08 by Janusz Grabowski, Grabowski, J., Alexei Kotov +3 · 1 citation
Mathematics · #13N10 #17B40 #17B56 #17B66 #58A50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1011.1804
openalex publication_date 2010/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds. We also prove that the group of automorphisms of such a Lie superalgebra is a semi-direct product of the subgroup induced by the supermanifold diffeomorphisms and another subgroup which consists of automorphisms determined by even superdivergences. These superdivergences are proven to exist on any supermanifold and their local form is explicitly described as well