On derivations of the heisenberg algebra

Derivations of the Heisenberg algebraH 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 algebraD(H) of all derivations ofH are distinguished, and their properties are studied. It is shown that the algebraH interpreted as a Lie algebra (with the commutator as the Lie bracket) forms a one-dimensional central extension ofD(H). Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118. No. 2 pp. 163–189, February, 1999.