On analogs of some classical group theoretical results in Poisson algebras

• Published in: Доповіді НАН України
• Date: 2021
• Main Authors: Kurdachenko, L.A., Pypka, A.A., Subbotin, I.Ya.
• Format: Article
• Language: English
• Published: Видавничий дім "Академперіодика" НАН України 2021
• Subjects: Математика
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/180515
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On analogs of some classical group theoretical results in Poisson algebras / L.A. Kurdachenko, A.A. Pypka, I.Ya. Subbotin // Доповіді Національної академії наук України. — 2021. — № 3. — С. 11-16. — Бібліогр.: 15 назв. — англ.

We investigate the Poisson algebras, in which the n-th hypercenter (center) has a finite codimension. It was established that, in this case, the Poisson algebra P includes a finite-dimensional ideal K such that P/K is nilpotent (Abelian). Moreover, if the n-th hypercenter of a Poisson algebra P ov...