Frequency spectra of short-period variations of cosmic ray

Frequency spectra for different periods of solar activity were calculated by 5-minutes data of a neutron super-monitor, (altitude 3340 m, cutoff rigidity is 6, 7 GV, counting rate is about 4.5.10 per hour). It was shown that shifting of the spectrum power from low-frequency range to high-frequency range takes place from minimum to maximum of the solar activity. It was reliably distinguished the peak with 160-minutes period coincided with the period of the Sun's atmosphere oscillation and some types of geomagnetic pulsation by the method of accumulation of the frequency spectra. It was conducted the comparison of cosmic ray spectra with spectra of geomagnetic field for the same point of the registration and at the same period

A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable

This is an old paper put here for archeological purposes. It is proved that a finite-dimensional Lie algebra over a field of characteristic p>5, that can be written as a vector space (not necessarily direct) sum of two nilpotent subalgebras, is solvable. The same result (but covering also the cases of low characteristics) was established independently by V. Panyukov (Russ. Math. Surv. 45 (1990), N4, 181-182), and the homological methods utilized in the proof were developed later in arXiv:math/0204004. Many inaccuracies in the English translation are corrected, otherwise the text is identical to the published version.Comment: v2: minor change

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen