The first cohomology groups of infinite dimensional Lie algebras

DOI10.3792/pjaa.56.197zbMath0464.58025OpenAlexW2073161092WikidataQ115219980 ScholiaQ115219980MaRDI QIDQ5904807

Nobutada Nakanishi

Publication date: 1980

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.56.197

zbMATH Keywords

first cohomology group with adjoint representationfirst cohomology groups of infinite dimensional Lie algebrasinfinite dimensional intransitive Lie algebras whose transitive parts are infinite and simpleinfinite dimensional transitive flat Lie algebras

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) Cohomology of Lie (super)algebras (17B56)

Cites Work

• On the intransitive Lie algebras whose transitive parts are infinite and primitive
• Cohomologies of Lie algebras of vector fields with coefficients in adjoint representations. Foliated case
• A Jordan-Hölder decomposition for a certain class of infinite dimensional Lie algebras
• The Cohomology of Transitive Filtered Modules. I: The First Cohomology Group