The analogs of Riemann and Penrose tensors on supermanifolds

Abstract

The Spencer cohomology of certain graded Lie superalgebras are completely computed. This cohomology is interpreted as analogs of Riemann and Penrose tensors on supermanifolds. The results make it manifest that there is no simple generalization of Borel-Weil-Bott's theorem for Lie superalgebras.

71 pp, LaTeX. The paper expounds the results of my eight papers that appeared mainly in not very accessible journals and proceedings

Cited by in corpus (10)

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• Minkowski superspaces and superstrings as almost real-complex supermanifolds
• Holonomy of supermanifolds
• Irreducible complex skew-Berger algebras
• Lie superalgebra structures in cohomology spaces of Lie algebras with coefficients in the adjoint representation
• Defining relations for classical Lie algebras of polynomial vector fields
• Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix
• Homogeneous irreducible supermanifolds and graded Lie superalgebras
• Two problems in the theory of differential equations