On the structure of graded symplectic supermanifolds and Courant algebroids

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dc.creatorRoytenberg, Dmitry
dc.date2002-03-12
dc.date.accessioned2026-07-07T04:46:59Z
dc.date.available2026-07-07T04:46:59Z
dc.descriptionThis paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating to such a bundle a graded symplectic supermanifold ((M,Ω)), with (\textrm{deg}(Ω)=2). Conversely, every such manifold arises in this way. We describe the algebra of functions on (M) in terms of (E) and show that ``BRST charges'' on (M) correspond to Courant algebroid structures on (E), thereby constructing the standard complex for the latter as a generalization of the classical BRST complex. As an application of these ideas, we prove the acyclicity of ``higher de Rham complexes'', a generalization of a classic result of Fröhlicher-Nijenhuis, and derive several easy but useful corollaries.
dc.description17 pages; to appear in the proceedings of the Conference on Quantization, Deformations and New Homological and Categorical Methods in Mathematical Physics
dc.identifierhttps://arxiv.org/abs/math/0203110
dc.identifierhttp://arxiv.org/abs/math/0203110
dc.identifierQuantization, Poisson Brackets and Beyond, Theodore Voronov (ed.), Contemp. Math., Vol. 315, Amer. Math. Soc., Providence, RI, 2002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63544
dc.subjectSymplectic Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.subject53D05; 81T70
dc.titleOn the structure of graded symplectic supermanifolds and Courant algebroids
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