Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
Manin pairs and moment maps
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abstract
A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, that generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are quasi-hamiltonian. These moment maps take values in the homogeneous space D/G. We prove an analogue of the hamiltonian reduction theorem for quasi-Poisson group actions, and we study the symplectic leaves of the orbit spaces of quasi-hamiltonian spaces.
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.