On the combinatorics of the graph-complex.
type: Item
instance of: scholarly article
title: On the combinatorics of the graph-complex.
zbMATH Open document ID: 1061.17022
DOI: 10.1016/S1631-073X(02)02204-5
author: Bodo Lass
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-01-01T00:00:00Z
review text: In [The Gelfand Mathematical Seminars 1990--1992 (ed. L.~Corwin et al.), Birkhäuser, 173--187 (1993; Zbl 0821.58018)], \textit{M. Kontsevich} introduced a certain graph-complex whose cohomology coincides with the cohomology of the Lie algebra of Hamiltonian vector fields (on the even space). This construction could be extended to the Lie (super)algebra of Hamiltonian vector fields on the odd space, yielding another graph-complex (it seems that the preprint of Kontsevich and Shoikhet the author is referring to, does not exist, at least at the time of writing of this review). In this paper, it is shown, in a purely combinatorical way, that the cohomology of these two graph-complexes coincide, which yieds coincidence of cohomology of corresponding Lie (super)algebras. It would be interesting to find a direct proof of the latter fact not appealing to graph-complexes, and, according to Feigin (quoted by the author), this seems to be a difficult question.
reviewed by: Pasha Zusmanovich
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 18G35
zbMATH DE Number: 1744390
zbMATH Keywords: Lie algebra of Hamiltonian vector fields
zbMATH Keywords: graph-complex
MaRDI profile type: Publication
cites work: Q3720764
cites work: Q4279791
cites work: Q5476030
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description: scientific article; zbMATH DE number 1744390