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 TMF: Year: Volume: Issue: Page: Find

 TMF, 1999, Volume 118, Number 2, Pages 163–189 (Mi tmf692)

On derivations of the Heisenberg algebra

V. V. Zharinov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Derivations of the Heisenberg algebra $\mathcal H$ and some related questions are studied. The ideas and the language of formal differential geometry are used. It is proved that all derivations of this algebra are inner. The main subalgebras of the Lie algebra $\mathfrak D(\mathcal H)$ of all derivations of $\mathcal H$ are distinguished, and their properties are studied. It is shown that the algebra $\mathcal H$ interpreted as a Lie algebra (with the commutator as the Lie bracket) forms a one-dimensional central extension of $\mathfrak D(\mathcal H)$.

DOI: https://doi.org/10.4213/tmf692

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English version:
Theoretical and Mathematical Physics, 1999, 118:2, 129–151

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Document Type: Article

Citation: V. V. Zharinov, “On derivations of the Heisenberg algebra”, TMF, 118:2 (1999), 163–189; Theoret. and Math. Phys., 118:2 (1999), 129–151

Citation in format AMSBIB
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\by V.~V.~Zharinov
\paper On derivations of the Heisenberg algebra
\jour TMF
\yr 1999
\vol 118
\issue 2
\pages 163--189
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\crossref{https://doi.org/10.4213/tmf692}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702872}
\zmath{https://zbmath.org/?q=an:1030.17503}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 2
\pages 129--151
\crossref{https://doi.org/10.1007/BF02557307}