Formal Poisson cohomology of twisted r-matrix induced structures
نویسندگان
چکیده
منابع مشابه
Formal Poisson Cohomology of Twisted r–Matrix Induced Structures
Quadratic Poisson tensors of the Dufour-Haraki classification read as a sum of an r-matrix induced structure twisted by a (small) compatible exact quadratic tensor. An appropriate bigrading of the space of formal Poisson cochains then leads to a vertically positive double complex. The associated spectral sequence allows to compute the Poisson-Lichnerowicz cohomology of the considered tensors. W...
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We introduce the concept of strongly r-matrix induced (SRMI) Poisson structure, report on the relation of this property with the stabilizer dimension of the considered quadratic Poisson tensor, and classify the Poisson structures of the Dufour-Haraki classification (DHC) according to their membership of the family of SRMI tensors. One of the main results of our work is a generic cohomological p...
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Poisson manifolds may be regarded as the infinitesimal form of symplectic groupoids. Twisted Poisson manifolds considered by Ševera and Weinstein [14] are a natural generalization of the former which also arises in string theory. In this note it is proved that twisted Poisson manifolds are in bijection with a (possibly singular) twisted version of symplectic groupoids.
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We propose a general approach to the formal Poisson cohomology of r-matrix induced quadratic structures, we apply this device to compute the cohomology of structure 2 of the Dufour-Haraki classification, and provide complete results also for the cohomology of structure 7. Key-words: Poisson cohomology, formal cochain, quadratic Poisson tensor, r-matrix 2000 Mathematics Subject Classification: 1...
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It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this is still true. We give an explicit description of the Ext-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential part of the Hochschild cohomology ring of a t...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2008
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-008-1016-z