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This article is cited in 3 scientific papers (total in 3 papers)
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 $\mathfrak D(\mathcal H)$.
Received: 21.07.1998
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
Linking options:
https://www.mathnet.ru/eng/tmf692https://doi.org/10.4213/tmf692 https://www.mathnet.ru/eng/tmf/v118/i2/p163
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