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 Tr. Mat. Inst. Steklova, 2000, Volume 228, Pages 61–75 (Mi tm491)

On the Cohomologies of the Heisenberg Algebras

V. V. Zharinov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper studies the cohomologies of the Heisenberg algebras as one-dimensional central extensions of commutative Lie algebras generated by nondegenerate 2-cocycles. Section 1 contains a general description of the cohomologies of one-dimensional central extensions of Lie algebras and typical examples. In Section 2, the general description is applied to explicitly evaluate the cohomologies of the Heisenberg algebra in important cases. Appendix describes the main properties of linear operations related to the generating 2-cocycle that are useful in particular calculations.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 52–66

Bibliographic databases:

Document Type: Article
UDC: 512.664

Citation: V. V. Zharinov, “On the Cohomologies of the Heisenberg Algebras”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Tr. Mat. Inst. Steklova, 228, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 61–75; Proc. Steklov Inst. Math., 228 (2000), 52–66

Citation in format AMSBIB
\Bibitem{Zha00} \by V.~V.~Zharinov \paper On the Cohomologies of the Heisenberg Algebras \inbook Problems of the modern mathematical physics \bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov \serial Tr. Mat. Inst. Steklova \yr 2000 \vol 228 \pages 61--75 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm491} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782572} \zmath{https://zbmath.org/?q=an:1003.17010} \transl \jour Proc. Steklov Inst. Math. \yr 2000 \vol 228 \pages 52--66 

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This publication is cited in the following articles:
1. Cagliero L., Tirao P., “The cohomology of the cotangent bundle of Heisenberg groups”, Advances in Mathematics, 181:2 (2004), 276–307
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