Reference : An inverse to the antisymmetrization map of Cartan and Eilenberg
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Physical, chemical, mathematical & earth Sciences : Mathematics
An inverse to the antisymmetrization map of Cartan and Eilenberg
Bordemann, Martin [Université de Haute Alsace, Mulhouse]
Riviere, Salim mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] chevalley-Eilenberg ; Hochschild ; Eulerian idempotent ; explicit contracting homotopy
This is a preprint of a joint work with M. Bordemann (UHA, Mulhouse), in which an explicit quasi-inverse to the antisymmetrization map between the Chevalley-Eilenberg complex of a Lie algebra and the Hochschild complex of its universal enveloping algebra is defined. Moreover, we provide an explicit formula for a contraction so that Hochschild homology appears as a deformation retract of Chevalley-Eilenberg homology. A third paragraph on quantification of coboundary Lie bialgebras, a bibliography, and an appendix should be added soon.

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