0000000000154616

AUTHOR

Walid Aloulou

showing 2 related works from this author

Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley–Harrison

2009

Resume Un prototype des algebres de Gerstenhaber est l'espace T poly ( R d ) des champs de tenseurs sur R d muni du produit exterieur et du crochet de Schouten. Dans cet article, on decrit explicitement la structure de la G ∞ algebre enveloppante d'une algebre de Gerstenhaber. Cette structure permet de definir une cohomologie de Chevalley–Harrison sur cette algebre. On montre que cette cohomologie a valeur dans R n'est pas triviale dans le cas de la sous algebre de Gerstenhaber des tenseurs homogenes T poly hom ( R d ) .

Mathematics(all)Mathematics::K-Theory and HomologyGeneral MathematicsMathematics::Quantum AlgebraMathematics::Rings and AlgebrasAlgèbres différentielles graduéesHumanitiesMathematics::Algebraic TopologyAlgèbres homotopiquesCohomologieCogèbresMathematicsBulletin des Sciences Mathématiques
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Chevalley cohomology for aerial Kontsevich graphs

2013

Let $T_{\operatorname{poly}}(\mathbb{R}^d)$ denote the space of skew-symmetric polyvector fields on $\mathbb{R}^d$, turned into a graded Lie algebra by means of the Schouten bracket. Our aim is to explore the cohomology of this Lie algebra, with coefficients in the adjoint representation, arising from cochains defined by linear combination of aerial Kontsevich graphs. We prove that this cohomology is localized at the space of graphs without any isolated vertex, any "hand" or any "foot". As an application, we explicitly compute the cohomology of the "ascending graphs" quotient complex.

Pure mathematicsMathematics (miscellaneous)Mathematics::K-Theory and HomologyMathematics::Quantum Algebra05C90Equivariant cohomology53D50Chevalley cohomologyTopologyKontsevich graphsCohomology17B56Mathematics
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