On cohomology of the Lie algebra of pseudodifferential symbols on a circle

DOI10.1007/BF02362639zbMath1009.17507OpenAlexW2060033967WikidataQ115392420 ScholiaQ115392420MaRDI QIDQ1356295

Claude Roger, Boris A. Khesin

Publication date: 3 April 2001

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02362639

zbMATH Keywords

cohomologyGelfand-Fuks cohomologyGodbillon-Vey classKhesin-Kravchenko theoremLie algebra of pseudodifferential symbols on a circle

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Cohomology of Lie (super)algebras (17B56) Classifying spaces for foliations; Gelfand-Fuks cohomology (57R32)

Cites Work

• A central extension of the algebra of pseudodifferential symbols
• Application of the cohomology of graded Lie algebras to formal deformations of Lie algebras
• The algebra of Weyl symmetrised polynomials and its quantum extension
• Déformation du crochet de Poisson sur une variété symplectique
• On the cohomology of the Lie algebra of Hamiltonian vector fields
• The cohomologies of the lie algebra of the vector fields in a circle
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